bluuebunny/crossref_metadata_2025 huggingface dataset:
A class of continuum models with no phase transitions
Authors: Klein David
Published: July 2002

For a restricted family of classical grand canonical continuum interactions, it is proved that the Gibbs state is unique at all temperatures and fugacities. The interactions considered are not translation invariant except in the one-dimensional case.
Kepler problem with a magnetic monopole
Authors: Cordani Bruno
Published: July 2002

It is shown that the usual moment map J: T*(R3−{0})]so*(2,4) of the Kepler problem can be generalized to include the magnetic term of the Dirac monopole.
Relation between the supertableaux of the supergroups OSP(2‖2) and SU(1‖2)
Authors: Gourdin Michel
Published: July 2002

The classification and the interpretation of the Young supertableaux of the orthosymplectic group OSP (2‖2) are given. A comparison is made with the supertableaux of the superunitary group SU(1‖2) taking advantage of the isomorphism of the corresponding superalgebras.
Petrov type D perfect-fluid solutions in generalized Kerr–Schild form
Authors: Martín J. , Senovilla J. M. M.
Published: July 2002

Generalized Kerr–Schild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.
Gravitational solutions, including radiation, for a perturbed light beam
Authors: Nackoney Raymond W.
Published: July 2002

Linearized field equations and solutions are derived for a perturbed sheet beam of light. The work is based on an exact solution of a collimated beam in the geometrical limit. The linearized field changes of the initially curved background metric can be put, with the help of the harmonic conditions, into a normal coordinate form. These six normal coordinates satisfy six linearized, inhomogeneous, field equations in three variables. Stationary solutions include divergent beams. Gravitational waves propagating opposite to the beam’s flux are found to be confined to a region about the propagation axis of the beam, much as is experienced in wave guides. Radiative cases can be produced by large angle scattering of light and are discussed in terms of their effect on an ideal optical antenna. The effect is one that grows linearly with time. The growth time is prohibitively long for the most energetic systems that can be realistically considered in the foreseeable future.
Large rectangular random matrices
Authors: Cicuta G. M. , Molinari L. , Montaldi E. , Riva F.
Published: July 2002

Models with a multiplet of field variables arranged into rectangular matrices, in the limit of infinite dimensions of the matrices, are studied. In zero-dimensional space (where the problem is a combinatorial one) a closed solution is given that improves the one previously known. In arbitrary space dimension a symmetry is described that connects rectangular models with vector models.
Weight-2 zeros of 3j coefficients and the Pell equation
Authors: Louck J. D. , Stein P. R.
Published: July 2002

All weight-2 zeros of the Wigner 3j coefficients may be obtained from the quadratic Diophantine equation known as Pell’s equation. These zeros may then be classified by the orbits of a discrete, infinite-order subgroup of the Lorentz group SO(1,1). This is carried out by transforming the ‘‘polynomial part’’ of a weight-2 3j coefficient to Pellian form and obtaining the fundamental zeros numerically. The relation of this polynomial to a family of binary quadratic forms is also given, together with a discussion of the invariance group.
Generalized Lorentz transformation for an accelerated, rotating frame of reference
Authors: Nelson Robert A.
Published: July 2002

An exact, explicit coordinate transformation between an inertial frame of reference and a frame of reference having an arbitrary time-dependent, nongravitational acceleration and an arbitrary time-dependent angular velocity is given. This transformation is a generalization of the Lorentz transformation and is obtained in two steps. First, the Minkowski metric is transformed under an intermediate coordinate transformation to obtain a new set of noninertial metric coefficients in which one can easily identify the Thomas precession, as well as the expression for the acceleration of the moving frame with respect to the instantaneous rest frame in terms of the acceleration as seen from a stationary inertial frame. Second, a rotation of axes is performed to absorb the Thomas precession and to add an ordinary spatial rotation. The coordinate transformation obtained by combining these effects is nonlinear, since certain terms involve time integrals, and leads to the appropriate space-time metric for an accelerated, rotating frame of reference. It is shown that the usual forms of the Lorentz transformation are contained as special cases of this result.
The group-theoretical classification of the 11-dimensional classical homogeneous Kaluza–Klein cosmologies
Authors: Demiański M. , Golda Z. , Sokol/owski L. M. , Szydl/owski M. , Turkowski P.
Published: July 2002

In the context of the classical Kaluza–Klein cosmology the generalized Bianchi models in 11 dimensions are considered. These are space-times whose spacelike ten-dimensional sections are the hypersurfaces of transitivity for a ten-dimensional isometry group of the total space-time. Such a space-time is a trivial principal fiber bundle P(M,G7), where M is a four-dimensional physical space-time with an isometry group G3 (of a Bianchi type) and G7 is a compact isometry group of the compact internal space. The isometry group of P is G10=G3⊗G7, hence all the generalized Bianchi models are classified by enumerating the relevant groups G7. Due to the compactness of G7 the result is astonishingly simple: there are three distinct homogeneous internal spaces in addition to the 11 ordinary Bianchi types for M.
Classical mechanics with respect to an observer’s past light cone
Authors: Derrick G. H.
Published: July 2002

This work is motivated by the fact that it is impossible for an observer to know at time t0 all the initial data of a system, if that data is specified in the conventional manner on the spacelike surface t=t0. A Hamiltonian formulation for classical mechanics, first given by Dirac, is exploited, in which dynamical variables are specified by their values on an observer’s past light cones. Starting from initial data given on the past light cone of an observer at some initial space-time point, the values of the variables on the observer’s current past light cone are given by a canonical transform of the initial data. The method is illustrated for a spinless particle of mass m, which is either free or interacts with an external electromagnetic field. The remarkable result is obtained that the dynamics of this classical one-particle spin-0 system can be formulated in terms of a Dirac-like spinor, whose four components are formed from the generalized coordinates and momenta.
A class of models of the universe filled with multidimensional objects
Authors: Chmielowski Piotr
Published: July 2002

An extension of Friedmann–Robertson–Walker models to the case of universes filled with perfect dust of multidimensional objects is investigated in this paper. It is shown that the internal space scale factor can become very small due to cosmological evolution regardless of the dimension of this space. This result is similar to those of flat [W. Kopczynski, Phys. Rev. D 36, 3589 (1987)] or vacuum [P. Turkowski and K. Maslanka, Gen. Relativ. Gravit. 19, 611 (1987)] models.
On a class of eigenfunction identities for Hill operators
Authors: Sachs Robert L.
Published: July 2002

Two very general identities are proved involving the eigenfunctions of two Hill operators and the spectrum of a third. Various specializations lead to a number of identities involving squares and fourth powers of the periodic eigenfunctions.
A theory of amplitudes
Authors: Gudder Stanley
Published: July 2002

A stochastic framework for quantum mechanics is presented in which the elements are measurements and amplitudes. The resulting structure provides three stochastic levels. At the bottom level are the sample points. These may be unobservable, in general. At the next level are the outcomes of measurements. The amplitude of an outcome is computed by summing the amplitudes of the sample points resulting in that outcome upon a measurement. At the highest level are the events of a measurement. The probability of an event is computed by summing the moduli squared of the amplitudes for the outcomes comprising that event. Using these guidelines, various probabilities, conditional probabilities, and expectations are defined. Superpositions of amplitude functions are investigated and superselection sectors are shown to occur in a natural way. The framework is illustrated in various mathematical models such as spin- (1)/(2) models, the two-slit experiment, and phase space quantum mechanics. Finally, a theory of discrete Feynman amplitudes is presented
Cohomology of the structure sheaf of real and complex supermanifolds
Authors: Bartocci Claudio , Bruzzo Ugo
Published: July 2002

The cohomology of the structure sheaf of real and complex supermanifolds is studied. It is found to be nontrivial (also in the real case), unless the supermanifold is De Witt, i.e., it is a fiber bundle on an ordinary manifold with a vector fiber. As a consequence, the Dolbeault theorem can be extended only to complex De Witt supermanifolds. The relevance of the nontrivial cohomology of the structure sheaf to the classification of complex line superbundles is discussed. The relationship between the Picard group of a complex De Witt supermanifold and the Picard group of its body is shown.
Alternative Lagrangians for spherically symmetric potentials
Authors: Crampin M. , Prince G. E.
Published: July 2002

A new, geometrical account of the existence of alternative (s-equivalent) Lagrangians is given for a particle moving in three-dimensional Euclidean space under the influence of a central force. The fact that the Lagrangian for this familiar problem is not unique was pointed out by Henneaux and Shepley [J. Math. Phys. 23, 2101 (1982)]: the present analysis makes the reasons for the phenomenon more transparent than theirs.
Complex structure on a real Hilbert space and symplectic structure on a complex Hilbert space
Authors: Sharma C. S.
Published: July 2002

Alternative ways of complexifying a real Hilbert space and quaternionizing a complex Hilbert space are described. The work gives some insight into why even though in the finite-dimensional case a complex Hilbert space when viewed as a real Hilbert space and a quaternionic Hilbert space when viewed as a complex Hilbert space have twice their original dimensions, the degrees of freedom of the linear operators remain unchanged. Many ramifications are discussed, among them the reconciliation of the linearity of the adjoint of a semilinear (antilinear) map from one complex Hilbert space to another with the semilinearity (antilinearity) of the adjoint of a semilinear (antilinear) map from one complex Hilbert space to itself. Groundwork is prepared for the study of the noncommutative algebra of additive operators on a quaternionic Hilbert space.
The hyperspin structure of unitary groups
Authors: Holm Christian
Published: July 2002

A sequence of homogeneous, isotropic, and compact solutions to the empty space hypergravity equations [D. Finkelstein, S. R. Finkelstein, and C. Holm, Phys. Rev. Lett. 59, 1265 (1987); S. R. Finkelstein, Ph.D. thesis, Georgia Institute of Technology, 1987 (unpublished)] is studied. These solutions are hyperspin manifolds constructed from unitary groups UN:=U(N,C) and describe static compact Einstein universes of the Kaluza–Klein type with Finslerian geometry. By taking the universal covering group of UN an N2-dimensional manifold with topology R×SUN is obtained, where the Abelian group R is the time axis and SUN provides a compact homogeneous spatial part. To describe the Finslerian geometry of these manifolds the Cartan–Penrose exterior calculus is extended from spinors to hyperspinors and the Maurer–Cartan equations are applied to obtain the hyperspin structure of UN. Hyperspin geometry seems to be a consistent alternative to the usual Riemannian geometry for spaces with internal dimensions, which deserves further study.
Irreducible *-representations of the Lie superalgebras B(0,n) with finite-degenerated vacuum. II
Authors: Blank J. , Havlíc̆ek M.
Published: July 2002

The method presented in the first part of this work is applied to the superalgebra B(0,2). Two families of irreducible *-representations of this superalgebra and its real form osp(1,4) are constructed explicitly in terms of differential operators on the Hilbert space L2(M̃)⊗CN of N-component vector functions Ψ: M̃→CN:(i) the family {πJ:J=0,1,...} of massless representations with N=2, M̃=R+×(−π,π)×R+, the dimension of the vacuum subspace of πJ being J+1; (ii) the family {π(ϑ)0:ϑ>0} of massive representations such that π(ϑ)0↾so(3,2) equals the direct sum of three irreducible representations of so(3,2). This family is characterized by N=4, M̃=R+×(0,π)×R+ and nondegenerated vacuum. It is also shown that all the remaining massive representations form a system of families {π(ϑ)J:ϑ>J/2}, J=1,2,..., with N=4(J+1), (J+1)-fold degenerated vacuum and common M̃=R+×(0,π)×R+.
Equivalence of transfer matrices
Authors: Novotny M. A.
Published: July 2002

Three theorems dealing with transfer matrices in statistical mechanical systems are proved. The theorems state that the nonzero eigenvalues of transfer matrices formed through various prescriptions are identical. Hence it is possible to ascribe a physical meaning to all the eigenvalues of a transfer matrix, not just to the few largest eigenvalues. The first theorem states that the transfer matrix formed by building a system M layers at a time has as its only nonzero eigenvalues the eigenvalues of the transfer matrix formed by building the M layers of the system one at a time. This theorem relates the product of two nM×nM M-layer transfer matrices to the product of M one-layer M×M transfer matrices. The second theorem states that one of the nM×nM M-layer transfer matrices (for M>1) has only one nonzero eigenvalue. A procedure for finding this eigenvalue and all eigenvectors is given. The third theorem generalizes the first to the case where the chosen layering is not an integer multiple of the interaction length.
Minimal models of U(1) conformal current algebra
Authors: Furlan P. , Sotkov G. M. , Stanev Ya.
Published: July 2002

A detailed study of the degenerate representations of the U(1)×U(1) conformal current algebra and field-theoretical models based on it is presented. The main peculiarity of these models is that they contain an infinite set of fields with unfixed anomalous dimensions. Simple fusion rules for these fields are found, and their four-point functions are calculated explicitly. The case of Thirring-like two-dimensional models is discussed in detail.
Wronskians, geometry, and some general solutions to the nonlinear Liouville-like PDE’s
Authors: Plebański Jerzy F.
Published: July 2002

The formal properties of n-dimensional Wronskians and their geometric interpretation enable one to construct explicit analytic solutions to some nonlinear partial differential equations (PDE’s) that generalize the Liouville equation φxy =e2φ. The studied PDE’s are (a) ℒmF =const, (b) ℒmF =G, ℒmG =F, and (c) ℒm(ℒmF ) =const, where ℒm is the nonlinear differential operation ℒmF: =det(∂kx∂lyF ), with k,l=0,1,...,m. Some nontrivial formal properties of the composition of the ℒm’s are established.
Solutions of Maxwell’s equations with boundary conditions on the hyperplane z−c
t=0
Authors: Hillion Pierre
Published: July 2002

In homogeneous free space the electromagnetic field may be represented by a second rank spinor, each component of which is a solution of the wave equation. This makes it possible to solve the boundary value problem for the electromagnetic field when the data given on the hyperplane z−ct=0 are entire functions. Two particular cases of boundary conditions that are not entire functions and that lead to a relativistic solution of Young’s experiment are discussed.
A quantum WKB approximation without classical trajectories
Authors: Molzahn F. H.
Published: July 2002

The time evolution of a coherent state is studied in the limit ℏ→0, for a spinless nonrelativistic quantum system in Euclidean space with smooth bounded time-dependent scalar interaction v(x,t). The lowest-order WKB approximation is derived rigorously, complete with an explicit bound on its L2-norm error over a specified finite time interval. The method is based on a constructive series representation of the classical action, thereby avoiding the need to analyze the behavior of classical trajectories. The amplitude of the initial states considered is neither assumed to be of rapid decrease, nor to depend on ℏ.
Location of essential spectrum of intermediate Hamiltonians restricted to symmetry subspaces
Authors: Beattie Christopher , Ruskai Mary Beth
Published: July 2002

A theorem is presented on the location of the essential spectrum of certain intermediate Hamiltonians used to construct lower bounds to bound-state energies of multiparticle atomic and molecular systems. This result is an analog of the Hunziker–Van Winter–Zhislin theorem for exact Hamiltonians, which implies that the continuum of an N-electron system begins at the ground-state energy for the corresponding system with N−1 electrons. The work presented here strengthens earlier results of Beattie [SIAM J. Math. Anal. 16, 492 (1985)] in that one may now consider Hamiltonians restricted to the symmetry subspaces appropriate to the permutational symmetry required by the Pauli exclusion principle, or to other physically relevant symmetry subspaces. The associated convergence theory is also given, guaranteeing that all bound-state energies can be approximated from below with arbitrary accuracy.
Perturbative coherence in field theory
Authors: Aldrovandi R. , Kraenkel R. A.
Published: July 2002

The basic field equations of a field theory are not always derivable from a Lagrangian. Lagrangian theories are perturbatively coherent, in the sense that they have well-defined vertices. Non-Lagrangian theories may be coherent or not. Coherent theories are, in principle, quantizable by perturbative methods. The general condition for a theory to have well-defined vertices is given.
Application of perturbation theory to the damped sextic oscillator
Authors: Srivastava Sunita , Vishwamittar
Published: July 2002

Perturbation theory for the anharmonic oscillator with large damping has been used to solve the equation of motion for the damped sextic oscillator. The results so obtained are compared with the values found through numerical integration of the equation of motion.
Superconformal algebras and Clifford algebras
Authors: Hasiewicz Z. , Thielemans K. , Troost W.
Published: July 2002

It is shown that superconformal Lie superalgebras contain a Clifford algebra structure. This is used to present a classification of these algebras under the following assumptions: only fields with (half-)integer conformal dimension between 2 and 1/2 , and a nonzero central element. It turns out that the number of supersymmetry generators must be less than or equal to 4. More generally, the so(N) series, as well as some nonassociative algebras connected to S7, also have a natural place in this Clifford algebra framework.
The causal geometry of twistor space
Authors: Low Robert J.
Published: July 2002

The problem of classifying the nature of the vector connecting a pair of points in Minkowski space is examined within the twistor theoretic framework. Two approaches are considered, one algebraic and the other geometric. The latter of the two is studied in some detail, providing some insight into the relation between the causal structure of Minkowski space and the geometry of projective twistor space.
Higher-order space-time contacts and equivalence
Authors: Maia M. D. , Roque W. L.
Published: July 2002

It is shown that two d-dimensional space-times, which make a contact of order d(d+1)/2, are locally equivalent in the sense that they represent the same local gravitational field.
A necessary and sufficient condition for convergence to equilibrium in Kolmogorov systems
Authors: Calzetta Esteban
Published: July 2002

A necessary and sufficient condition is established for a state to converge to equilibrium in a dynamical system described as a Kolmogorov system. Because the time reversal of a state converging to equilibrium does not necessarily share this property, this opens the possibility of spontaneous breaking of time reversal symmetry.
Analytic observations for the d=1+ 1 bridge site (or single-step) deposition model
Authors: Evans J. W. , Kang H. C.
Published: July 2002

Some exact results for a reversible version of the d=1+1 bridge site (or single-step) deposition model are presented. Exact steady-state properties are determined directly for finite systems with various mean slopes. These show explicitly how the asymptotic growth velocity and fluctuations are quenched as the slope approaches its maximum allowed value. Next, exact hierarchial equations for the dynamics are presented. For the special case of ‘‘equilibrium growth,’’ these are analyzed exactly at the pair-correlation level directly for an infinite system. This provided further insight into asymptotic scaling behavior. Finally, the above hierarchy is compared with one generated from a discrete form of the Kardar–Parisi–Zhang equations. Some differences are described.
On nontrivial interactions and complete integrability of soliton equations
Authors: Beals Richard , Konopelchenko Boris
Published: July 2002

Interacting multisoliton solutions of soliton equations are constructed using the inverse spectral transform and their asymptotics are analyzed. The Hamiltonian structure is obtained in terms of scattering data and the complete integrability of solutions of the N-wave equations with nontrivial interactions is proved.
How overdetermined are the generalized self-duality relations?
Authors: Tchrakian D. H. , Chakrabarti A.
Published: July 2002

It is shown that the self-duality equations of the generalized Yang–Mills (GYM) models are overdetermined except when they are subjected to the spherical or axial symmetry. It is also found that the Bogomol’nyi equations on Rd, of the GYM–Higgs (GYM–H) models descended from the GYM system on Rd×S8−d, are overdetermined for d=3,4,5, and 6 only.
The gravity of three-forms
Authors: Xanthopoulos Basilis C. , Zannias Thomas
Published: July 2002

Solutions of Einstein’s equations are examined when a particular class of closed three-form fields is taken as a source. The choice of source is motivated by developments in particle physics indicating the possible existence of physical fields described by three-forms. After summarizing basic dynamical equations and some properties, attention is focused on two particular configurations: (1) static, spherically symmetric, self-gravitating, three-form fields; and (2) homogeneous and isotropic geometries coupled to three-forms. For the spherically symmetric case, there exists two mutually exclusive sets of effective equations, solutions which describe static, spherically symmetric, self-gravitating axion fields. For the one class of the effective equations, a two-parameter family of asymptotically flat solutions of the Einstein axion field equations have been constructed. The axionic black hole solution of Bowick et al. [Phys. Rev. Lett. 61, 2823 (1988)] is also recovered as a special case of this class. For the other set of equations, only a special solution has been constructed. Its properties and global structure are discussed at length. For the case of axions coupled to homogeneous and isotropic geometries, explicit solutions of the relevant equations have also been constructed. In particular, for the case where the hypersurfaces of homogeneity are either flat or characterized by negative curvature, a global solution is obtained. It represents an ever expanding universe originating from a spacelike curvature singularity. For the case of a closed universe, local solutions have been constructed, which in principle can be patched to yield a global solution. Nevertheless, by employing them, the singularity structure of this solution was able to be analyzed. It behaves in the same manner as the previous two cases.
Establishing the Riemannian structure of space-time by means of light rays and free matter waves
Authors: Audretsch Jürgen , Lämmerzahl Claus
Published: July 2002

As compared with axiomatic schemes based on the paths of massive point particles, a constructive approach based on the classical limit of the wave mechanics of matter fields has a particular advantage: The locally approximately plane waves do not only define matter rays, but can in addition be subject to interference measurements. These, in contrast to the free-fall experiments, are sensitive to the mass. This makes it possible to further specify the geometry of space-time. Light rays reveal a conformal structure of the space-time manifold. It will be shown that if, in addition, in each point of space-time locally approximately plane matter waves can be realized that are free and massive, the space-time is a Riemann space.
A counterexample in coagulation theory
Authors: Buffet E. , Werner R. F.
Published: July 2002

Two models of interacting polymers, both within Smoluchovski’s theory, are considered. The first model has purely diagonal reaction rates and shows gelation. The second model has the same diagonal reaction rates but also some nondiagonal ones; the second model does not show gelation. Hence, contrary to intuition, gelation can be destroyed by an increase in the reaction rates. The example also disproves a conjecture stating that the diagonal reaction rates are the determining factor for gelation.
Anomaly meltdown
Authors: Gajdzinski C. , Streater R. F.
Published: July 2002

It is shown that at nonzero temperature it is possible that anomalies in representations of symmetry groups and gauge groups, present at zero temperature, disappear. Several examples are given. Thus the idea that anomalies in baryon currents might have caused the baryon imbalance in the early hot universe needs reconsideration.
Super twistor realization of unitary super representations of U(p,q‖N)
Authors: Pilato Alex
Published: July 2002

This paper is concerned with demonstrating that the twistor realization of the ladder representation of U(p,q) can be generalized to super representations of U(p,q‖N). This is achieved by considering the generalization of twistor elementary states to a super algebraic category. Unitarity of these super representations follows from the positive definiteness of a super twistor scalar product constructed in this paper. Although generalizations of the ladder representations have been well studied by other means, it will be shown that the super twistor generalization is especially natural and merits special investigation.
On the bi-Hamiltonian structure, strong and hereditary operator of symmetries for a new nonlinear system
Authors: Purkait S. , Chowdhury A. Roy
Published: July 2002

The bi-Hamiltonian structure, strong, and hereditary operator for symmetries for a new nonlinear integrable system have been deduced by the procedure of Fourier analysis and small amplitude expansion. The recursion operator for the gradient of conserved quantities has been written down. An important feature of this approach is that, it is possible to obtain several solutions of the equation determining the symplectic operator. But unfortunately one cannot construct the strong (hereditary) operator from all such pairs of solution. Only for some special solutions it was possible to do so. In these cases the strong and hereditary property can be proven explicitly. In the following, examples of operators belonging to both of these classes will be cited.
Dynamical stability and thermodynamic stability in irreversible thermodynamics
Authors: Chen M.
Published: July 2002

By constructing a nonlinear model, the relationship between thermodynamic stability and dynamical stability in classical irreversible thermodynamics is investigated. It will be proven that the thermodynamic equilibrium state is thermodynamically stable if it is dynamically asymptotically stable.
Comments on ‘‘Relations between hyperspherical harmonic transformations and generalized Talmi–Moshinsky transformations’’ [J. Math. Phys. 3
1, 1621 (1990)]
Authors: Raynal Jacques
Published: July 2002

In the Appendix of a recent article, [X.-h. Liu, J. Math. Phys. 31, 1621 (1990)] on the relations between hyperspherical harmonics and two-body oscillator wave functions, Liu presented ‘‘explicit’’ expressions of the coefficients of the transformation between the two basis as a quadruple sum for three-body systems and a sextuple sum for the four-body problem. These coefficients have been known for a long time to be a single sum equivalent to a 3F2 series of argument unity, quite similar to the 3-jm symbols of SU(2) for the three-body system. For the four-body system, they are the product of two such expressions.
Contact symmetry algebras of scalar second-order ordinary differential equations
Authors: Mahomed F. M. , Leach P. G. L.
Published: July 2002

There is a natural link between contact symmetries (symmetries that leave invariant the first-order contact form) and first integrals of a given second-order ordinary differential equation. It will be shown that the contact symmetry algebra of a general second-order ordinary differential equation is infinite dimensional and it is generated by the functionally independent first integrals of the equation. Moreover, the contact symmetry algebras of second-order equations admitting one, two, three, and eight point symmetries are obtained.
Translationally invariant global charges in a local collision theory for massless particles
Authors: Strube Dieter
Published: July 2002

Within the framework of a Wightman field theory of massless particles, translationally invariant generators Q of symmetry transformations defined as integrals over the time component of conserved local currents are considered. It is shown that Q is defined on massless asymptotic multiparticle states. It is additively determined by its action on one-particle states and commutes with the S matrix. If the asymptotic fields are scalar it is shown that Q is represented on one-particle states by a polynomial in the derivatives.
Noisy fractals
Authors: García-Pelayo Ricardo , Schieve William C.
Published: July 2002

An analytical study of affine contractive iterated function systems (IFS’s) is done in which noise is put in between each iteration of the maps. Since any contractive Poincaré map can be approximated arbitrarily well by IFS’s, this is also a study of how noise modifies repellers or attractors of dissipative systems. In particular the scale at which the noise erases the fractal detail is found.
Analytic solution of the Bardeen–Cooper–Schrieffer gap equation in one, two, and three dimensions
Authors: van der Walt D. M. , Quick R. M. , de Llano M.
Published: July 2002

Analytic expressions for the Bardeen–Cooper–Schrieffer (BCS) gap of a many-electron system with the BCS model interaction are obtained in one, two, and three dimensions in the weak coupling limit, but for arbitrary interaction width ν≡ℏωD/EF, 0<ν<∞. Here ℏωD is the maximum energy of a force-mediating boson, and EF is the Fermi energy (which is fixed by the electronic density). Our results address both phononic (ν≪1) as well as nonphononic (e.g., exciton, magnon, plasmon, etc.) pairing mechanisms where the mediating boson energies are not small compared with EF, provided weak electron–boson coupling prevails. The essential singularity in coupling, sometimes erroneously attributed to the two-dimensional character of the BCS model interaction with ν≪1, is shown to appear in one, two, and three dimensions before the limit ν→0 is taken.
Null infinity does not carry massive fields
Authors: Helfer Adam D.
Published: July 2002

It is shown that all representations of the Poincaré group on homogeneous vector bundles on null infinity are massless. This shows that null infinity cannot be an initial-data surface for massive fields.
Cylindrically symmetric viscous universes
Authors: Patel L. K. , Dadhich Naresh
Published: July 2002

The cylindrically symmetric cosmological models with viscous fluid having the Kasnerian time evolution are considered herein. It turns out that the ‘‘no-matter’’ limit of geodetic viscous universes, which can as well be looked upon as string-dust universes, is the nonflat empty Kasner space–time. It is proposed that the universe may be born with the Kasner geometry at t=0 with matter in the form of viscous fluid, then it may follow the path: geodetic to nongeodetic and finally to the radiation phase when viscosity is fully worn out. Solutions to describe each phase separately are given.
Existence and structure of infinitely degenerate zero-energy ground states of a Wess–Zumino-type model in supersymmetric quantum mechanics
Authors: Ogurisu Osamu
Published: July 2002

It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model with the superpotential V(z)=λeαz(λ ∈ C\{0},α≥0) has infinitely many bosonic zero-energy ground states and no fermionic zero-energy ground states [A. Arai, J. Math. Phys. 30, 1164 (1989)]. In this article, these results are extended to a more general model. The main results include the following: (1) identification of the spectra of the Hamiltonian H of the model; (2) non-Fredholmness of a supercharge of the model, which is a Dirac-type operator; (3) existence of infinitely many bosonic zero-energy states of H; (4) nonexistence of fermionic zero-energy states of H.
Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space–times with horizons
Authors: Kay Bernard S.
Published: July 2002

Let ω be a state on the Weyl algebra over a symplectic space. We prove that if either (i) the ‘‘liberation’’ of ω is pure or (ii) the restriction of ω to each of two generating Weyl subalgebras is quasifree and pure, then ω is quasifree and pure [and, in case (i) is equal to its liberation, in case (ii) is uniquely determined by its restrictions]. [Here, we define the liberation of a (sufficiently regular) state to be the quasifree state with the same two point function.] Results (i) and (ii) permit one to drop the quasifree assumption in a result due to Wald and the author concerning linear scalar quantum fields on space–times with bifurcate Killing horizons and thus to conclude that, on a large subalgebra of the field algebra for such a system, there is a unique stationary state whose two point function has the Hadamard form. The paper contains a number of further related developments including: (a) (i) implies a uniqueness result, e.g., for the usual free field in Minkowski space. We compare and contrast this with other known uniqueness results for this system. (b) A similar pair of results to (i) and (ii) is proven for ‘‘quasiFree’’ states and ‘‘libeRations’’ where the definition of quasiFree differs from what we call here quasifree in that nonvanishing one point functions are permitted, and the libeRation of a state is defined to be the quasiFree state with the same one and two point functions. (c) We derive similar results for the canonical anticommutation relations.
Two theorems on the kernel of Faddeev equations for the scattering of three charged particles and some applications
Authors: Latypov D. M. , Mukhamedzhanov A. M.
Published: July 2002

The operator TcG0, which represents the singular part of the kernel of the Faddeev equations for the scattering of charged particles above breakup threshold, is studied. The operator is considered in two classes of functions. The functions from the first class have an on-shell limit and the functions from the second class have an on-shell singularity of a type (z−P 2)iτ, τ∈R. In both classes the most singular part of TcG0 is found to be proportional to a delta function. In order for Faddeev equations to have a solution in the second class, τ is shown to be equal to the sum of the Sommerfeld parameters of all two-body subsystems.
Two singular potentials: The space-splitting effect
Authors: Oseguera U. , de Llano M.
Published: July 2002

The quantum mechanical problem of a particle moving in one dimension (1D) under the influence of a singular potential is reexamined. An attractive delta function potential of infinite strength and the 1D Coulomb potential is considered in particular. In both cases the singularity acts as an impenetrable barrier, thus dividing space into two independent regions. Analysis of the scattering states gives results in agreement with this conclusion. The implications that the bound states of the 1D Coulomb potential cannot be classified according to parity, even though the potential is symmetric, is also discussed herein.
Lower bounds for quartic anharmonic and double-well potentials
Authors: Burrows B. L. , Cohen M. , Feldmann Tova
Published: July 2002

Rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the Schrödinger equation with quartic anharmonic and symmetric double-well potentials of the form V(A,B)=Ax2/2+Bx4(B≥0) are presented. This procedure exploits some exactly soluble model potentials and appears to be of quite general utility.
Maximal reductions in the Baker–Hausdorff formula
Authors: Kolsrud Marius
Published: July 2002

A preliminary expression for the Baker–Hausdorff formula is found up to ninth order, i.e., a series expansion of z in terms of multiple commutators, where ez=exey with x and y noncommuting, up to ninth degree in x,y. By means of complete sets of linear relations between multiple commutators maximal reduction of the number of different multiple commutators in the series are obtained.
Metric of two arbitrary Kerr–Newman sources located on the symmetry axis
Authors: Manko V. S. , Martín J. , Ruiz E.
Published: July 2002

An exact asymptotically flat axisymmetric solution of the Einstein–Maxwell equations representing the exterior field of two arbitrary Kerr–Newman masses located on the symmetry axis is constructed in explicit form. In a particular case, when the solution describes two identical Kerr–Newman sources, simple analytical formulas are obtained which allow a straightforward analysis of the equilibrium of two charged rotating masses. Some arguments are given in favor of the possibility of the balance of stationary black holes due to their gravitational spin–spin interaction.
Graded contractions and the conformal group of Minkowski space–time
Authors: Tolar J. , Trávníček P.
Published: July 2002

All Z2×Z2-graded contractions preserving the space isotropy with grading induced by the Π (space inversion) and Θ (time reversal) automorphisms of the Lie algebras A3 and so(4,2) are listed. Some properties of these contractions are discussed.
Representation of the five-dimensional harmonic oscillator with scalar-valued U(5) ⊇ SO(5) ⊇ SO(3)–coupled VCS wave functions
Authors: Rowe D. J. , Hecht K. T.
Published: July 2002

Vector coherent state methods, which reduce the U(5) ⊇ SO(5) ⊇ SO(3) subgroup chain, are used to construct basis states for the five-dimensional harmonic oscillator. Algorithms are given to calculate matrix elements in this basis. The essential step is the construction of SO(5) ⊇ SO(3) irreps of type [v,0]. The methodology is similar to that used in two recent papers except that one-dimensional, as opposed to multidimensional, vector-valued wave functions are used to give conceptually simpler results. Another significant advance is a canonical resolution of the SO(5) ⊇ SO(3) multiplicity problem.
Phase-amplitude dynamics of the nonlinear Schrödinger equation with rapid forcing
Authors: Moroz Irene M. , Newton Paul K.
Published: July 2002

We consider the initial value problem for the forced one dimensional nonlinear Schrödinger equation (NLS), where the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced NLS are sought by expressing the dependent variable in modulus-phase form and expanding in powers of a small parameter, which is inversely related to the forcing time scale. This system is similar to a forced eikonal-transport system arising in nonlinear geometrical optics. We focus on the effect that the forcing has on the NLS standing solitary wave. Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function. A general conclusion of this work is that the effect of the forcing on the phase variable is quite important in determining the overall structure of the forced solitary wave.
Scalar field inhomogeneous cosmologies
Authors: Feinstein A. , Ibáñez J. , Labraga P.
Published: July 2002

Some exact solutions for the Einstein field equations corresponding to inhomogeneous G2 cosmologies with an exponential-potential scalar field, which generalize solutions obtained previously, are considered. Several particular cases are studied and the properties related to generalized inflation and asymptotic behavior of the models are discussed.
Bender–Wu formula for the Zeeman effect
Authors: Briet Philippe
Published: July 2002

We prove the Bender–Wu formula in the case of magnetic Schrödinger operators under general considerations on the potential. We also give a bound on the behavior of the perturbation series coefficients for the ground state energy.
A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors
Authors: Bohm A. , Antoniou I. , Kielanowski P.
Published: July 2002

The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in-state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.
Unification of the Dirac and Einstein Lagrangians in a tetrad model
Authors: Reifler Frank , Morris Randall
Published: July 2002

In a recent article all classical tensor systems which admit Fermi quantization are characterized as those having unitary Lie–Poisson brackets. Examples include Euler’s tensor equation for a rigid body and Dirac’s equation in tensor form. In this article it is shown that the tensor form of the Dirac Lagrangian can be derived from a tetrad formulation of a Kaluza–Klein model, which unifies the Dirac and Einstein Lagrangians. In this formulation, the isometric modes of the tetrad propagate as fermions, whereas the self-adjoint modes propagate as gravitons. An analogy is made with the rigid and elastic modes of a deformable body, where the rigid modes are Fermi quantized and the elastic modes are Bose quantized. However, unlike a deformable body for which the Euclidean metric is positive definite, fermion and graviton modes are not generally separable, unless the gravitational fluctuations are limited by a certain bound. It is shown that this bound applies whenever bispinors are defined in a general relativistic framework. That is, the bound does not depend on whether bispinors or tensors are used to describe the fermion modes.
Generating functional approach to multichannel parallel relaxation with application to the problem of direct energy transfer in fractal systems with dynamic disorder
Authors: Vlad Marcel Ovidiu , Mackey Michael C.
Published: July 2002

A model for multichannel parallel relaxation is suggested based on the following assumptions: (a) an individual channel is characterized by a set of continuous state variables; the corresponding relaxation rate is a function of the state variables as well as of the time interval for which the channel is open; (b) the number of channels is a random variable described by a correlated point process defined in the space of state parameters of an individual channel. Analytical expressions for the generating functional of the overall relaxation rate and for the average survival function are derived in terms of the generating functional of the point process. The general formalism is applied to the problem of direct energy transfer from excited donors to acceptors in fractal systems with dynamic disorder. It is assumed that the number of acceptors obeys a Poissonian distribution law with a constant average density in a df-dimensional fractal structure embedded in a ds-dimensional Euclidean space (ds=1,2,3) and that an individual relaxation rate is an inverse power function of the distance between the acceptor and the donor molecules.

The dynamic disorder is described in terms of three different functions: the rate ω(t) of opening of a channel at time t, the attenuation function φ(t) of the reactivity of an individual channel at time t, and the probability density ψ(t) of the time interval within which a channel is open. Several particular cases corresponding to different functions ω(t), φ(t), and ψ(t) are investigated. The static disorder corresponds to a survival function of the stretched exponential type exp[−(Ωt)β] with 1≳β≳0. For very strong dynamic disorder there is no attenuation of reactivity, the opening time is infinite and the survival function is given by a compressed exponential exp[−const.t1+β], 1≳β≳0. The other cases analyzed correspond to a slowly decreasing attenuation function and to an exponential distribution of the opening time, respectively; for them the efficiency of relaxation is between the ones corresponding to the two extreme cases of static and very strong dynamic disorder. The general conclusion is that the passage from static to the dynamic disorder results in an increase of the efficiency of the relaxation process.
Fuzzy mass relations for the Higgs
Authors: Iochum Bruno , Kastler Daniel , Schücker Thomas
Published: July 2002

The noncommutative approach of the standard model produces a relation between the top and the Higgs masses. We show that, for a given top mass, the Higgs mass is constrained to lie in an interval. The length of this interval is of the order of m2τ/mt.
On the dynamics of characteristic surfaces
Authors: Frittelli Simonetta , Newman Ezra T. , Kozameh Carlos N.
Published: July 2002

We formulate the vacuum Einstein equations as differential equations for two functions, one complex and one real on a six-dimensional manifold, ℳ×S2, with ℳ eventually becoming the space–time and the S2 becoming the sphere of null directions over ℳ. At the start there is no other further structure available: the structure arising from the two functions. The complex function, referred to as Λ[ℳ×S2], encodes information about a sphere’s worth of surfaces through each point of ℳ. From knowledge of Λ one can define a second rank tensor on ℳ which can be interpreted as a conformal metric, so that the ‘‘surfaces’’ are automatically null or characteristics of this conformal metric. The real function, Ω, plays the role of a conformal factor: it converts the conformal metric into a vacuum Einstein metric. Locally, all Einstein metrics can be obtained in this manner. In this work, we fully develop this ‘‘null surface version of general relativity (GR):’’ we display, discuss and analyze the equations, we show that many of the usual geometric quantities of GR (e.g., the Weyl and Ricci tensors, the optical parameters, etc.) can be easily expressed in terms of the Λ and Ω, we study the gauge freedom and develop a perturbation theory. To conclude, we speculate on the significance and possible classical and quantum uses of this formulation.
Braided geometry of the conformal algebra
Authors: Majid Shahn
Published: July 2002

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the q→1 scaling limit of the braided adjoint action or R-commutator of q-Minkowski space on itself. We also describe the q-deformed conformal algebra in R-matrix form and its quasi-* structure.