bluuebunny/crossref_metadata_2025 huggingface dataset:
Exponential perturbations of the harmonic oscillator
Authors: Maioli Marco
Published: March 2003

The operators H(β) = p2+x2+βerx(r∈R{0}) in L 2(R) are studied. The spectrum is discrete for ‖argβ‖<π, the eigenvalues admit an asymptotic expansion as ‖β‖→0, and they have no Bender-Wu type singularities in the analytic continuation to any punctured sector of a logarithmic Riemann surface. For β′<0,H(β′) defines a symmetric operator with deficiency indices (1,1) and all its self-adjoint extensions have discrete spectrum; however, any eigenvalue of H(β′), when continued to β′<0, can be interpreted as a resonance of the problem.
Partition combinatorics and multiparticle scattering theory
Authors: Kowalski K. L. , Polyzou Wayne N. , Redish Edward F.
Published: March 2003

The recently developed combinatoric methods for handling partition-labeled operators in N-particle scattering theory are studied from an abstract point of view. The relation of these methods to approaches of the cluster/cumulant type in many areas of mathematical physics is pointed out. The concept of connectedness is defined abstractly and the mathematical structure of the partition lattice is considered in detail. Many of the useful results of combinatoric scattering theory are shown to be natural expressions of properties of the partition lattice. The conditions on these results can then be stated with precision. A number of new operator theorems are also obtained by means of applying simple extensions and analogs of the known properties of the partition lattice.
Local transverse-traceless tensor operators in general relativity
Authors: Monroe David K.
Published: March 2003

Two flat-space transverse-traceless tensor operators can be used to construct initial data for numerical solutions of the gravitational field equations. One of these operators is related to the conformal curvature 3-tensor and is shown to exist in a large class of nonflat 3-spaces. The second operator enjoys no such liberty. Important applications to gravitational wave scattering are suggested. It is argued that the number of operators available on a particular 3-space is related to the number of gravitational field modes that are excited in the space.
Renormalization group convergence for small perturbations of Gaussian random fields with slowly decaying correlations
Authors: Malyshev V. A. , Tirozzi B.
Published: March 2003

We find that certain random fields obtained by perturbing Gaussian fields with a self-interaction potential have the same limit properties as do the random fields of statistical mechanics.
Diagonalizability of the longitudinal sector of the functional integral in massive SU (2) Yang–Mills theories via topological contributions
Authors: Ktorides C. N.
Published: March 2003

The problem of longitudinal sector diagonalizability of the functional integral in massive SU (2) Yang–Mills theories is revisited. A new decomposition law of a massive SU (2) vector field into transverse and longitudinal parts is proposed which takes into account the more recently discovered topological properties of SU (2) gauge theories. After establishing the credibility of this decomposition law, it is shown how it leads to the diagonalizability of the longitudinal sector of the functional integral. This result is related to the problem of the existence of the zero-mass limit in massive SU (2) Yang–Mills theories.
Toward exact solutions of the nonlinear Heisenberg–Pauli–Weyl spinor equation
Authors: Mielke Eckehard W.
Published: March 2003

In color geometrodynamics fundamental spinor fields are assumed to obey a GL(2f,C)⊗GL(2c,C) gauge-invariant nonlinear spinor equation of the Heisenberg–Pauli–Weyl type. Quark confinement, assimilating a scheme of Salam and Strathdee, is (partially) mediated by the tensor ’’gluons’’ of strong gravity. This hypothesis is incorporated into the model by considering the nonlinear Dirac equation in a curved space-time of hadronic dimensions. Disregarding internal degrees of freedom, it is then feasible, for a peculiar background space-time, to obtain exact solutions of the spherical bound-state problem. Finally, these solutions are tentatively interpreted as droplet-type solitons and remarks on their interrelation with Wheeler’s geon construction are made.
Algebraically special Yang–Mills solutions without sources
Authors: Fulp R. O. , Sommers Paul , Norris L. K.
Published: March 2003

We consider source-free Yang–Mills solutions for which the curvature is decomposable in the sense that the curvature 2-form is the product of a single Lie-algebra-valued function and a real 2-form. If the curvature is everywhere nonnull (or null with twisting rays), then the solution is a connection in a principal fiber bundle, which is reducible to a source-free Maxwell principal bundle. All such solutions are therefore readily obtained, locally or globally, from Maxwell solutions. Our analysis uses the Ambrose–Singer theorem to show that the holonomy group is one-dimensional. A principal bundle-with-connection is reducible to the holonomy subbundle of any point, and, in this case, since the holonomy group is one-dimensional, the reduced bundle has the structure of a Maxwell bundle. On the other hand, if the curvature is null and twist-free on a full neighborhood of some point, then the bundle need not be reducible. The holonomy group is generally the entire gauge Lie group. The solutions can still be constructed locally from Maxwell solutions, there being extra freedom in the construction over regions where the Maxwell field is algebraically null with twist-free rays. We extend all these results to the class of solutions for which the self-dual curvature is (complex) decomposable. These are all the solutions of type D and type N in the classification of Anandan and Tod.
Quasigroup construction and first class constraints
Authors: Batalin I. A.
Published: March 2003

A generalization of the Lie group construction is proposed wherein the composition law depends, apart from the parameters of the transformations composed, also on the transformed variables. This construction is met, in particular, on the hypersurfaces specified by the first class constraints in phase space.
A criterion for completeness of Casimir operators
Authors: Berdjis F.
Published: March 2003

We give a criterion for a set of Casimir operators of any semisimple Lie algebra to be an algebraically independent generating set of the algebra of the Casimir operators. The criterion is applied to supply complete sets for the Casimir operators of Al, Bl, Cl , and Dl . With the aid of a method to construct some Casimir operators we then furnish complete sets for the Casimir operators of the exceptional Lie algebras using the criterion.
Casimir operators for F4, E6, E7, and E8
Authors: Berdjis F. , Beslmüller E.
Published: March 2003

We construct explicitly algebraically-independent generating sets for the Casimir operators and the invariants of the Weyl groups and adjoint groups of the exceptional Lie algebras F4, E6, E7, and E8.
The analytical properties of the off-shell T matrix for infinite rank nonlocal separable potentials
Authors: Daskaloyannis C.
Published: March 2003

Analytical expression and uniform bounds for the lth partial wave off-shell T matrix are derived for infinite rank separable potentials. It is proved that Fredholm’s alternative can be used to solve the Lipmann–Schwinger equation in some cases of noncompact nonlocal potentials in the strong Lp topology.
Global definition of nonlinear sigma model and some consequences
Authors: Percacci R.
Published: March 2003

The (nonlinear) sigma model is defined as a field theory whose configurations are sections of a nontrivial fiber bundle over space–time. The action functional is a generalization of the ’’energy’’ used in the theory of harmonic maps. This definition requires minimal coupling to a Yang–Mills field, and the solutions of the coupled equations exhibit spontaneous symmetry breaking. It is shown that in a Higgs phenomenon making use of a sigma model instead of the Higgs fields, no scalars would survive symmetry breaking.
Dynamical Noether invariants for time-dependent nonlinear systems
Authors: Kaushal R. S. , Korsch H. J.
Published: March 2003

Dynamical invariants are derived for time-dependent systems with nonlinear equations of motion including nonharmonic damped systems. The concept of a dynamical algebra is discussed and its utility for the construction of dynamical invariants for nonharmonic systems is demonstrated. Finally we show the existence of dynamical invariants for some nonlinear quantum systems.
Electromagnetism and the holomorphic properties of spacetime
Authors: Salingaros Nikos
Published: March 2003

The Cauchy–Riemann equations of holomorphy are extended to fields in higher-dimensional spaces in a framework of Clifford algebras. The equations of holomorphy in Minkowski spacetime turn out to be the Maxwell equations in vacuum. The Lorentz gauge condition is a result of the holomorphy. Sources can be included in an extension of the residue theorem, where charges correspond to the residues.
Radiative degrees of freedom of the gravitational field in exact general relativity
Authors: Ashtekar Abhay
Published: March 2003

The radiative degrees of freedom of the gravitational field are isolated by analyzing the structure available at null infinity, 𝒥It is shown thay they are coded in certain equivalence classes {D} of connections; all information about gravitational radiation can be extracted from the curvature tensors of these connections directly on 𝒥 without any reference to the interior of space–time. The space of classical vacua—i.e., of {D} with trivial curvature—is analyzed. It is shown that the quotient ST/T of the BMS supertranslation group by its translation subgroup acts simply and transitively on this space. The available structure is compared with that of gauge theories. Since the entire discussion can be carried out on𝒥 without any reference to the interior, it suggests a new approach to quantum gravity. This approach will be presented in detail in a subsequent paper.
Sp(6) states in an SU(3)×U(1) basis
Authors: Gaskell R. , Rosensteel G. , Sharp R. T.
Published: March 2003

We find all missing label operators and also a complete set of analytic nonorthonormal basis states for the group–subgroup Sp(6)⊇SU(3)×U(1), both for the compact version of Sp(6) and for the noncompact Sp(6,R) relevant to the symplectic nuclear collective model.
Generating functions for G2 characters and subgroup branching rules
Authors: Gaskell R. , Sharp R. T.
Published: March 2003

The G2 character generator is given; with its help generating functions are derived for branching rules for G2 irreducible representations reduced according to its maximal semisimple subgroups.
On generalized torsion tensor fields and the reduced fiber bundle
Authors: Cianci Roberto
Published: March 2003

The reduction of a connection form ρ from a fiber bundle P to a subbundle Q is examined in detail; defining generalized torsion forms, we show how the usual Maurer–Cartan structural equations have to be modified. Examples and applications to classical general relativity and gauge theories are outlined.
Representations of the groups GL(n,R) and SU(n) in an SO(n) basis
Authors: Gruber Bruno , Klimyk Anatoli U.
Published: March 2003

The explicit form for the infinitesimal operators and the (finite) matrix elements with respect to an SO(n) basis is obtained for the representations of the most degenerate series of the group SL(n,R), and for the irreducible unitary representations of the group SU(n) with highest weight (M,0,...,0).
Non-self-adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. I. Direct spectral and scattering problems
Authors: Asano Naruyoshi , Kato Yusuke
Published: March 2003

The Zakharov and Shabat equation for the scattering problem is studied: The estimates, analytical properties, and asymptotic expansions of the Jost solution are presented for a general class of the potentials Q(x) not vanishing at infinity. The existence of the similarity transformation is also shown. For Q(x) vanishing at infinity, the continuous part of the spectrum doubly degenerates. However, nonvanishing (finite) asymptotic values of Q(x) dissolve the degeneracy completely. The expansion theorem is given in C02(R) and for a class of Q(x) we prove that the Zakharov and Shabat equation yields a non-self-adjoint spectral operator in the Hilbert space in the sense of Dunford and Schwartz.
Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach
Authors: Cacuci Dan G.
Published: March 2003

Concepts of nonlinear functional analysis are employed to investigate the mathematical foundations underlying sensitivity theory. This makes it possible not only to ascertain the limitations inherent in existing analytical approaches to sensitivity analysis, but also to rigorously formulate a considerably more general sensitivity theory for physical problems characterized by systems of nonlinear equations and by nonlinear functionals as responses. Two alternative formalisms, labeled the ’’forward sensitivity formalism’’ and the ’’adjoint sensitivity formalism,’’ are developed in order to evaluate the sensitivity of the response to variations in the system parameters. The forward sensitivity formalism is formulated in normed linear spaces, and the existence of the Gâteaux differentials of the operators appearing in the problem is shown to be both necessary and sufficient for its validity. This formalism is conceptually straightforward and can be advantageously used to assess the effects of relatively few parameter alterations on many responses. On the other hand, for problems involving many parameter alterations or a large data base and comparatively few functional-type responses, the alternative adjoint sensitivity formalism is computationally more economical. However, it is shown that this formalism can be developed only under conditions that are more restrictive than those underlying the validity of the forward sensitivity formalism. In particular, the requirement that operators acting on the state vector and on the system parameters must admit densely defined Gâteaux derivatives is shown to be of fundamental importance for the validity of this formalism. The present analysis significantly extends the scope of sensitivity theory and provides a basis for still further generalizations.
T matrix for Coulomb-nuclear admixtures
Authors: Talukdar B. , Mallick N. , Kundu M. , Panigrahi R. N.
Published: March 2003

A model is proposed for calculating the T matrix for Coulomb-distorted separable nuclear potentials without the use of the Gell-Mann–Goldberger two-potential theorem. Analytical expressions for the Jost function and T matrix are presented for the Yamaguchi plus screened Coulomb potential treated in the Ecker–Weizel approximation.
Four Euclidean conformal group approach to the multiphoton processes in the H-atom
Authors: Gazeau Jean-Pierre
Published: March 2003

A compact analytical form, suitable for any analytic continuation, is obtained for the following bound–bound N-photon transition matrix element, Inlm→n′l′m′ ≡〈n′l′m′ ‖ ∏i = 1N {p⋅εir⋅εi}eiki⋅ r ×G(Ei)‖nlm〉, where G(E) is the Coulomb Green’s function. We show that Inlm→n′l′m′ is a ’’linear superposition’’ of matrix elements 𝒯1(g)n′l′m′→nlm of some irreducible representation 𝒯1 of a semigroup G−1? contained in the four Euclidean conformal group G = SU*(4)≊SO0(1,5). This ’’linear superposition’’ is understood in the general framework of the theory of the distributions on a Lie group. The final result is a linear combination of special functions known as ’’generalized Euler functions.’’
Vacuum handles carrying angular momentum; electrovac handles carrying net charge
Authors: Friedman John L. , Mayer Steven
Published: March 2003

Nonsimply-connected spacetimes can have locally defined Killing vectors that are globally defined only up to sign (pseudovectors). We show the existence of asymptotically flat vacuum spacetimes which are axisymmetric (have a rotational Killing pseudovector), are topologically trivial outside a spatially compact region, and which nevertheless have nonzero angular momentum. An analogous construction establishes the existence of source-free Einstein–Maxwell spacetimes which are topologically trivial outside a spatially compact region and which nevertheless carry nonzero net electric charge. The existence of such spacetimes leads to a new variant of the combined positive energy-cosmic-censorship conjecture: Given an asymptotically flat vacuum or electrovac initial data set which is axisymmetric and geodesically complete, the asymptotic mass, charge Q, and angular momentum J satisfy m?[Q2+(J/m)2]1/2.
The form of Killing vectors in expanding ℋℋ spaces
Authors: Sonnleitner Stephanie A. , Finley J. D.
Published: March 2003

The Killing vector structure of those spaces of complexified general relativity known as expanding hyperheavens is investigated using the methods of spinor calculus. The Killing equations for all left-algebraically degenerate Einstein vacuum spaces are completely integrated. Using the available gauge freedom, the resulting homothetic and isometric Killing vectors are classified in an invariant way according to Petrov–Penrose type. A total of four distinct kinds of isometric Killing vectors and three distinct kinds of homothetic Killing vectors are found. A master Killing vector equation is found which gives the form that the Lie derivative of the metric potential function W must take in order that it admit a given Killing vector.
An exceptional type D shearing twisting electrovac with λ
Authors: García D. Alberto , Plebañski Jerzy F.
Published: March 2003

A new electrovac with λ type D solution and with both Debever–Penrose vectors aligned along the real eigenvectors of the electromagnetic field is presented. The principal null directions are shearing and twisting. The existence of this solution, endowed with an O(2,1,R) symmetry, requires λ<0.
A cluster expansion in field theory
Authors: Kowall James , Fried H. M.
Published: March 2003

A cluster expansion is proposed for the calculation of certain Green’s functions in field theory. The results presented are for λφ4 theory, expanded in the number of scalar closed loops through the introduction of the composite field, χ = i√λ/12 φ2. As an intermediate step, Feynman path integrals are used to perform the functional integration over the field degrees of freedom. The cluster expansion that results is equivalent to perturbation theory, but at lowest order sums up all the infrared behavior of the theory. Higher orders systematically include ultraviolet effects.
Similarity solutions of nonlinear Dirac equations and conserved currents
Authors: Steeb W. -H. , Erig W. , Strampp W.
Published: March 2003

Nonlinear Dirac equations in one space dimension and three space dimensions are studied. Using the continuous symmetries of the nonlinear Dirac equations we reduce the system of nonlinear partial differential equations to a system of nonlinear ordinary differential equations, applying group theoretical methods, and give solutions of these equations. Moreover, we determine conserved currents using the continuous symmetries of the nonlinear Dirac equation.
Symmetry of time-dependent Schrödinger equations. II. Exact solutions for the equation {∂x
x+2i∂t−2g2(t)x2−2g1(t)x −2g0(t)}Ψ(x, t) = 0
Authors: Truax D. Rodney
Published: March 2003

The maximal kinematical algebra of the Schrödinger equation {∂xx+2i∂t−2g2(t)x2−2g1(t)x−2 g0 (t)}Ψ(x, t) = 0 is known to be the Schrödinger algebra 𝓈1. The kinematical symmetries are realized as first-order differential operators in the space and time variables. A subalgebra 𝒢 of 𝓈1 is chosen and from 𝒢 and its invariants a complete set of commuting observables are constructed. The solution space of the Schrödinger equation is identified with the appropriate irreducible representation space of 𝒢. The wave functions, simultaneous eigenvectors of the compatible observables, are computed as explicit functions of space and time. The properties of a system with a potential V(x, t) = g2(t)x2+g1(t)x+g0(t) are discussed.
Ground state energy bounds for potentials ‖x‖ν
Authors: Crandall R. E. , Reno Mary Hall
Published: March 2003

A theory is developed from which both upper and lower analytic bounds on Schrödinger eigenvalues can be obtained. We propose a recursion algorithm with which ground energies for certain potentials can be rigorously bounded to arbitrary precision. These analytic and numerical methods, together with existing techniques, are applied to the ground state problem for power potentials ‖x‖ν, ν≳0.
On the structure of Coulomb-type scattering amplitudes
Authors: Gesztesy F.
Published: March 2003

On the basis of the Gell-Mann–Goldberger formula for Mo/ller operators we introduce a natural splitting of the total scattering operator S into the pure Coulomb scattering operator Sc plus a remainder S = Sc−2πiTsc, implying a decompostion of the total scattering amplitude f into the Coulomb scattering amplitude fc and a remaining part fsc f(k,ω,ω′) = fc(k,ω,ω′)+fsc(k,ω,ω′). Concerning continuity properties, etc., of fsc, close similarities between fsc and ordinary short-range amplitudes are proved. In particular, we introduce transition operators tsc(z) and show how to obtain fsc by an appropriate on-shell limit, thereby avoiding the notion of so-called Coulomb transition operators and the difficulties associated with them. Possible extensions of this approach to charged three-particle systems are also sketched.
Modified fourth-order Casimir invariants and indices for simple Lie algebras
Authors: Okubo Susumu
Published: March 2003

The fourth-order indices for Lie algebras have been defined and studied by Patera, Sharp, and Winternitz. We show that it may be more convenient to modify the original definition and that the modified fourth-order indices are intimately related to eigenvalues of symmetrized fourth-order Casimir invariants. Explicit expressions for these quantities are given and we also find a quartic trace identity involving the generic element of these Lie algebras. We discuss the triality principle for the Lie algebra D4 in connection with identical vanishing of the modified fourth-order index for this algebra.
Finite-size effects on the relativistic electrons in a Coulomb field. I
Authors: Ogata H. , Asai J.
Published: March 2003

The influence of the finite nuclear size and screening effects on the evaluation of the interaction matrix elements of the Dirac electron in the nuclear Coulomb field is manipulated into a closed analytic form. An application to the evaluation of the Bremsstrahlung cross section is discussed.
On the uniqueness of the energy–momentum tensor for electromagnetism
Authors: Kerrighan D. B.
Published: March 2003

For the case of a space–time manifold we show that the metric tensor and the well-known energy–momentum tensor for electromagnetism are the only symmetric, rank 2 tensor concomitants of an arbitrary bivector, and the metric whose divergences vanish whenever the bivector satisfies the source-free Maxwell equations.
Quantum tachyon in a Friedmann universe
Authors: Srivastava S. K.
Published: March 2003

The scalar wave equation of a primordial tachyon is investigated in a Friedmann universe of positive curvature containing different perfect fluids. Also the energy of a tachyon as well as the rate of emission of energy from a primordial tachyon in different models has been discussed.
Initial data and wave propagation in one-dimensional inhomogeneous cosmologies
Authors: Matzner Richard A. , Rosenbaum M. , Ryan M. P.
Published: March 2003

We consider the initial value problem and the short-time evolution of a system consisting of two Euclidean-homogeneous (Bianchi type I) cosmologies, each containing a homogeneous scalar field φ or a homogeneous electric field, abutted at the plane z=0. We show that a matching is possible, and discuss the evolution for a vacuum (φ=0) cosmology abutted to one with nonzero scalar field φ.
Local conformal-invariance of the wave equation for finite-component fields. I. The conditions for invariance, and fully-reducible fields
Authors: Bracken A. J. , Jessup Barry
Published: March 2003

The conditions for local conformal-invariance of the wave equation are obtained for finite-component fields, of Types Ia and Ib [in the terminology of Mack and Salam, Ann. Phys. 53, 174 (1969).] These conditions generate a set of locally invariant free massless field equations and restrict the relevant representation of the Lie algebra [(k4⊕d)⊕sl(2,C)] in the index space of the field to belong to a certain class. Those fully-reducible representations which are in this class are described in full. The corresponding Type Ia field equations include only the massless scalar field equation, neutrino equations, Maxwell’s equations, and the Bargmann–Wigner equations for massless fields of arbitrary helicity, and no others. In particular, it is confirmed [Bracken, Lett. Nuovo Cimento 2, 574 (1971)] that not all Poincaré-invariant sets of massless Type Ia field equations are conformal-invariant, contrary to some often-quoted results of McLennan [Nuovo Cimento 3, 1360 (1956)], which are shown to be invalid. It is also shown that in the case of a potential, the wave equation is never conformal-invariant in the strong sense (excluding gauge transformations).
Generalized quaternions and spacetime symmetries
Authors: Jantzen Robert T.
Published: March 2003

The construction of a class of associative composition algebras qn on R4 generalizing the well-known quaternions Q provides an explicit representation of the universal enveloping algebra of the real three-dimensional Lie algebras having tracefree adjoint representations (class A Bianchi type Lie algebras). The identity components of the four-dimensional Lie groups GL(qn,1) ⊆qn (general linear group in one generalized quaternion dimension) which are generated by the Lie algebra of this class of quaternion algebras are diffeomorphic to the manifolds of spacetime homogeneous and spatially homogeneous spacetimes having simply transitive homogeneity isometry groups with tracefree Lie algebra adjoint representations. In almost all cases the complete group of isometries of such a spacetime is isomorphic to a subgroup of the group of left and right translations and automorphisms of the appropriate generalized quaternion algebra. Similar results hold for the single class B Lie algebra of Bianchi type V, characterized by its ‘‘pure trace’’ adjoint representation.
Some comments on finite subgroups of SU(3)
Authors: Fairbairn W. M. , Fulton T.
Published: March 2003

A recently published set of finite subgroups of SU(3) is shown to contain some groups which are not subgroups of SU(3). The others are subgroups of one of the dihedral-like family of SU(3) subgroups Δ, of order 3n2. Some comments are made also on the structure of other finite subgroups previously listed.
Wigner approach to quantization. Noncanonical quantization of two particles interacting via a harmonic potential
Authors: Palev Tchavdar D.
Published: March 2003

Following the ideas of Wigner, we quantize noncanonically a system of two nonrelativistic point particles, interacting via a harmonic potential. The center of mass phase-space variables are quantized in a canonical way, whereas the internal momentum and coordinates are assumed to satisfy relations, which are essentially different from the canonical commutation relations. As a result, the operators of the internal Hamiltonian, the relative distance, the internal momentum, and the orbital momentum commute with each other. The spectrum of these operators is finite. In particular, the distance between the constituents is preserved in time and can take at most four different values. The orbital momentum is either zero or one (in units ℏ/2). The operators of the coordinates do not commute with each other and, therefore, the position of any one of the constituents cannot be localized; the particles are smeared with a certain probability in a finite space volume, which moves together with the center of mass. In the limit ℏ→0 the constituents ‘‘fall’’ into their center of mass and the composite system behaves as a free point particle.
Quantum and classical mechanics on homogeneous Riemannian manifolds
Authors: Emch Gérard G.
Published: March 2003

Starting from the axioms of quantum mechanics as formalized by the systems of imprimitivity for homogeneous Riemannian manifolds, the classical theory is derived as a consequence, complete with its phase space realized as the space of pure classical states, a generalized version of the Wigner–Moyal correspondence rule, the Jordan and Lie algebra structures of functions on the cotangent bundle, given by point-wise multiplication and Poisson bracket, and the momentum map. A comparison is also given of the quantum and classical dynamics and equilibrium statistical mechanics of free particles on compact manifolds of constant negative curvature.
Quantum evolution in the presence of additive conservation laws and the quantum theory of measurement
Authors: Ghirardi G. C. , Rimini A. , Weber T.
Published: March 2003

In this paper we derive in a completely rigorous way a family of inequalities holding for proper combinations of the squared norms of the states generated by the quantum evolution of a compound quantum system in the presence of additive conservation laws. The application of these inequalities to the quantum theory of measurement yields lower bounds for the malfunctioning of a measuring apparatus, which are valid under more general mathematical conditions and for a larger variety of physical situations than those considered up to now in the literature.
Constructing measures for path integrals
Authors: Daubechies Ingrid , Klauder John R.
Published: March 2003

The overcompleteness of the coherent states for the Heisenberg–Weyl group implies that many different integral kernels can be used to represent the same operator. Within such an equivalence class we construct an integral kernel to represent the quantum-mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine (Wiener) measures on continuous phase-space paths. To achieve this goal it is necessary to employ an expression for the classical action different from the usual one.
Properties of solutions for N-body Yakubovskii–Faddeev equations
Authors: Benoist-Gueutal P. , L’Huillier M.
Published: March 2003

We give a revised presentation of the Yakubovskii–Faddeev formalism based on a systematic study of the N-body system chain structure. Completeness properties of the corresponding equations in differential form are considered. The expressions of physical and spurious solutions are given in terms of the N-body asymptotic partition Hamiltonians eigenvectors.
On the invertibility of Mo/ller morphisms
Authors: Maassen Hans
Published: March 2003

Local perturbations of the dynamics of infinite quantum systems are considered. It is known that, if the Mo/ller morphisms associated to the dynamics and its perturbation are invertible, the perturbed evolution is isomorphic to the unperturbed one, and thereby shares its ergodic properties. It was claimed by V. Ya. Golodets [Theor. Math. Phys. 23, 525 (1975)] that the above condition holds whenever the observable algebra is asymptotically abelian for the unperturbed evolution, and the perturbed evolution has a KMS state. The present paper contains a counterexample to this statement, and a construction of a spatial representation of the Mo/ller morphisms.
On mapping approaches in axiomatic quantum field theory
Authors: Yao Te Hai
Published: March 2003

We here state a collection of results in axiomatic quantum field theory obtained under the general philosophy of ‘‘mapping approaches.’’ It is hoped that these results will stimulate further investigations along this direction, especially in connection with the problem of the existence and the construction of nontrivial four-dimensional quantum field theories.
The second Legendre transform for the weakly coupled P(φ)2 model
Authors: Cooper Alan , Feldman Joel , Rosen Lon
Published: March 2003

We prove the existence and analyticity of the second Legendre transform of the generating functional for Euclidean Green’s functions in the weakly coupled P(φ)2 model. The proof involves a bound on the partition function with a nonlocal quadratic source term. This bound also implies bounds on the Schwinger functions Sn( f1,..., fn) that are optimal with respect to both topology and n-dependence.
Explicit construction of the exceptional superalgebras F(4) and G(3)
Authors: DeWitt Bryce S. , van Nieuwenhuizen Peter
Published: March 2003

A general method for constructing the extension of an ordinary Lie algebra 𝒜0 to a superalgebra 𝒜0⊕𝒜1 is given, once one knows in which representation of 𝒜0 the odd generators 𝒜1 are. Explicit matrix representations for the superalgebras F(4) and G(3), and for ordinary algebras E8, F4, and G2 are presented.
Study of superluminal electromagnetic fields
Authors: Negi O. P. S. , Rajput B. S.
Published: March 2003

Behavior of Maxwell’s equations under imaginary and real superluminal Lorentz transformations respectively has been reexamined and the expression of a Lorentz force acting on an electric charge interacting with superluminal electromagnetic fields has been derived. It has been shown that in four-dimensional space-time as well as in six-dimensional space-time the electrically charged tachyon interacting with electromagnetic fields behaves neither as a purely electric charge nor as a purely magnetic monopole.
The differential geometric structure of general mechanical systems from the Lagrangian point of view
Authors: Hermann Robert
Published: March 2003

Several differential-geometric points of view on analytical mechanics of systems with a finite number of degrees of freedom are developed in generality, emphasizing Cartan’s calculus of differential forms and Ehresmann’s theory of jet spaces. The classical theory of Lagrange’s equations with external forces and constraints (‘‘holonomic’’ or ‘‘nonholonomic’’) is put into an invariant and coordinate-free form. The relation between this ‘‘Lagrangian’’ and the ‘‘Hamiltonian-symplectic’’ approach, which is that most extensively used in the contemporary mathematical physics literature, is also developed.
The equivalence of two approaches to the Feynman integral
Authors: Johnson G. W.
Published: March 2003

Two apparently quite different Banach algebras of functions have been introduced and studied recently in connection with the theory of the ‘‘Feynman integral.’’ The functions in both spaces have been shown to be ‘‘Feynman integrable,’’ but two different definitions of the ‘‘Feynman integral’’ were used. We show here that the two spaces are in fact isometrically isomorphic as Banach algebras where the correspondence is given by what is essentially an extension (or restriction) map. Further, the ‘‘Feynman integrals,’’ in the two different senses, of corresponding functions are equal. The equivalence between these two theories is surprisingly easy to prove but has a number of consequences for both theories. In the last section of the paper we give a few simple but useful consequences and make some remarks about our experience so far in using the equivalence.
Approximate methods for the solution of the Chandrasekhar H-equation
Authors: Kelley C. T.
Published: March 2003

We consider two methods of approximate solution to matrix valued analogs of the Chandrasekhar H-equation. We give conditions under which they converge. The first method is a generalization of approximation of the integral by a quadrature. The second is Newton’s method.
Structure of three-twistor particles
Authors: Lukács B. , Perjés Z. , Sebestyén Á. , Newman E. T. , Porter J.
Published: March 2003

The simplest physical system to have a nontrivial intrinsic structure in Minkowski space-time is a three-twistor particle. We investigate this structure and the two pictures of the particle as an extended object in space-time and as a point in unitary space. We consider the effect of twistor translations on the mass triangle defined by the partial center of mass points in space-time. Finally we consider the connections between twistor rotations and spin and we establish the spin deficiency formula.
Path integral for coherent states of the dynamical group SU(1,1)
Authors: Gerry Christopher C. , Silverman Steven
Published: March 2003

Path integrals over coherent states of the dynamical group (noninvariance group) SU(1,1) are constructed. From the continuous limit the relevant classical dynamics is extracted and is shown to take place in a curved phase space of the form of a Lobachevskii plane. Applications are made to the harmonic oscillator, a model of superfluid helium, the Morse oscillator, and the hydrogen atom. It is shown that when SU(1,1) is the relevant dynamical group the motion will appear oscillator-like on the Lobachevskii plane.
Cartan–Gram determinants for the simple Lie groups
Authors: Wu Alfred C. T.
Published: March 2003

The Cartan–Gram determinants for the simple root systems are evaluated for the simple Lie groups An, Bn, Cn, Dn, and Ek (k=6,7,8). The determinants satisfy a linear recursion relation which turns out to be the same for all these groups. For the En family, the Cartan–Gram determinant contains an explicit factor of (9−n) which vanishes for n=9 and is negative for n>9. This gives a simple explanation why the En family terminates at E8. The Cartan–Gram determinant affords a systematic explanation for the nonexistence of the forbidden Dynkin diagrams.
On a unified approach to transformations and elementary solutions of Painlevé equations
Authors: Fokas A. S. , Ablowitz M. J.
Published: March 2003

An algorithmic method is developed for investigating the transformation properties of second-order equations of Painlevé type. This method, which utilizes the singularity structure of these equations, yields explicit transformations which relate solutions of the Painlevé equations II–VI, with different parameters. These transformations easily generate rational and other elementary solutions of the equations. The relationship between Painlevé equations and certain new equations quadratic in the second derivative of Painlevé type is also discussed.
The equivalence problem for the heat equation
Authors: Strampp W.
Published: March 2003

In this note we ask for the classes of equations of the second order which can be transformed into the heat equation ut=uxx. To give a partial answer to the question we express the heat equation by differential forms and prolong it by the Estabrook–Wahlquist method. This is motivated by the fact that our analysis is based upon conservation laws for which ideals of differential forms are a very suitable framework. Necessary conditions are derived for deciding whether a given equation can be transformed by some invertible point transformation into the heat equation or into its prolongation. In particular, the prolongation method enables us to understand the connection of various equations to the heat equation.
Space–time memory functions and solution of nonlinear evolution equations
Authors: Nishigori Takeo
Published: March 2003

A new approach is presented for solving a certain class of nonlinear partial differential equations. A space–time memory function Λ(r,t) is introduced to exactly convert a given nonlinear evolution equation into the following linear form: (∂/∂t) f(r,t)=Ω(r) f(r,t) +∫t0dt′∫dr′Λ(r−r′,t−t′)f(r′,t′). A Markovian integro-differential operator Ω(r) and the memory function Λ(r,t) reflect the nonlinearity, and are determined depending on a given initial condition. The approach is useful if higher-order memory functions associated with Λ are insensitive to approximation. The Korteweg–de Vries equation is treated as an example. For certain initial profiles the memory function is shown to be identically zero, and we find exact linear partial differential equations leading to the single- and the two-soliton solution. In the case of the three-soliton solution, the second-order memory function vanishes exactly, and Λ(r,t) is found to be a single exponential function of t.
Langer’s method for weakly bound states of the Helmholtz equation with symmetric profiles
Authors: Johnston George L.
Published: March 2003

Use of the harmonic oscillator equation as the comparison equation in the application of Langer’s method to bound states of the Helmholtz equation, w″+k20g(z)w(z)=0, with symmetric profiles k20g(z), produces the WKB eigenvalue condition, which asserts the equality of the phase integral of the original equation between the turning points to (n+1/2)π. In the case of weakly bound states, this condition gives eigenvalue estimates of low accuracy. Use of the Helmholtz equation with the symmetric Epstein profile, G(x)=[Ẽ+U0(cosh αx)−2], as the comparison equation provides the basis for a convenient method to obtain eigenvalue estimates of substantially increased accuracy in the case of weakly bound states. In addition to the usual condition of equality of the phase integrals of the original and comparison equations between the turning points, the conditions k20g(0) =G(0) and k20g(∞) =G(∞) are imposed. An eigenvalue condition which is a simple generalization of the usual WKB eigenvalue condition is obtained. Its application to selected diverse examples of the Helmholtz equation indicates that it has a broad range of utility.
Direct and inverse scattering by a sphere of variable index of refraction
Authors: Eftimiu C.
Published: March 2003

It is shown that in cases with spherical symmetry, a Liouville transformation leads from the wave equation to a Schrödinger-like equation with energy-independent potential. The direct problem can be solved by iteration and the inverse problem by the Marchenko formalism. An exactly solvable example is given.
On the nonexistence of static solutions of the Einstein–Weyl equations in general relativity
Authors: Kolassis Charalampos A.
Published: March 2003

It is proved that the combined gravitational-neutrino equations in general relativity admit no nontrivial solutions in a static space-time provided that the energy density of the neutrino field is nonnull for all observers.
A class of solutions of the generalized Lund–Regge model
Authors: Ray Dipankar
Published: March 2003

A class of solutions are obtained for the generalized Lund–Regge model of Corones [J. Math. Phys. 19, 2431 (1978)] and its Euclidean counterpart. As a consequence, a new solution is noted for the original Lund–Regge model.
NUT 4-momenta are forever
Authors: Ashtekar Abhay , Sen Amitabha
Published: March 2003

The asymptotic structure of the gravitational field at null infinity is re-examined by allowing certain potentials to develop ‘‘wire singularities’’, keeping the physical fields smooth. This relaxation of the regularity conditions leads to the introduction of the Newman–Unti–Tamburino (NUT) 4-momentum which is the ‘‘magnetic’’ or the ‘‘dual’’ counterpart of the Bondi–Sachs 4-momentum. It is shown that, unlike the Bondi–Sachs 4-momentum, the NUT 4-vector is absolutely conserved even in the presence of gravitational radiation. Thus, while the gravitational field resembles the nonabelian Yang–Mills fields in its ‘‘electric’’ properties, it is analogous to the abelian Maxwell field in its ‘‘magnetic’’ properties. It is pointed out that gravitational fields with nonvanishing NUT 4-momenta may have a substantial role in quantum gravity even though they are not physically significant in classical general relativity.
Theory of nonlinear Langevin equation with quadratic noise
Authors: Wódkiewicz K.
Published: March 2003

A generalized Langevin equation with a multiplicative linear and quadratic Ornstein–Uhlenbeck stochastic noise is investigated. An exact generalized Fokker–Planck equation for this Langevin equation is obtained. This generalized Fokker–Planck equation has the form of an integro–differential equation. An exact form of the integral kernel is given in terms of an operator-valued matrix-continued fraction. In the limit of small fluctuations and short coherence time of the noise a standard Fokker–Planck equation with drift and diffusion is derived in a systematic way.
The occupational statistics for indistinguishable trimers on a 3×N lattice space
Authors: Hock J. L. , Licato P. E. , McQuistan R. B.
Published: March 2003

A 20 term recursion relation is derived that describes exactly the occupational degeneracy for trimers distributed on a 3×N lattice space. The associated generating functions, expectation, normalization, dispersion, and continuous representation are also developed and discussed.
On the convergence of reflectionless approximants to confining potentials
Authors: Stefanescu I. Sabba
Published: March 2003

We discuss the problem of the convergence of the reflectionless approximants VN(x), proposed bny Quigg, Rosner, and Thacker, to the true confining potential V(x), both for ‘‘wrong’’ [u′(0)=0] and ‘‘correct’’ [u(0)=0] boundary conditions. We show that, for any function φ(x) with continuous derivativce and compact support contained in (0,∞), ∫∞0φ(x)VN(x)dx →∫∞0φ(x)V(x)dx as N→∞, if V(x) is appropriately restricted. Namely, for ‘‘wrong’’ boundary conditions, V(x) should be such that the difference σ(E) between its spectral measure and the free one obeys ‖σδ(E)‖<const×E−ε, to a semiclassical estimate and, in this approximation, V(x)<Cx2−ε.
On the finiteness of the number of discrete eigenvalues in neutron transport theory
Authors: Cacuci Dan G.
Published: March 2003

This work examines the finiteness of the number of discrete eigenvalues occurring in neutron slowing down and transport in an infinite medium consisting of a single nuclide scattering elastically, isotropically, and with energy-independent cross sections. This finiteness is related to convergence conditions for the Legendre moments of the scattering function. It is shown that the convergence criterion obtained by Case for one-velocity neutron transport is not satisfied by hydrogen at large lethargies. A new convergence criterion, weaker than that of Case, is derived and shown to be satisfied by all nuclides, including hydrogen, at all lethargies. Although derived within the more general framework of energy-dependent transport, the new convergence criterion also holds for the Legendre moments of the scattering function in one-velocity transport.
Semiclassical calculation of a radial path integral
Authors: Gerry Christopher C. , Inomata Akira
Published: March 2003

A semiclassical method of evaluating a path integral for the central potential problem is presented. The Langer transformation r=ex, when applied properly to a radial path integral, brings about an appropriate range of integration and the desired angular momentum modification (l(l+1))1/2ℏ→(l+1/2)ℏ. The resultant path integral becomes assessable by semiclassical calculations. The method is seen to work for obtaining the exact energy spectra of the isotropic harmonic oscillator and the hydrogen atom bound states.
Convergence of the T-matrix approach in the potential scattering
Authors: Ramm A. G.
Published: March 2003

Convergence of the T-matrix scheme is established for the potential scattering.
Linkages and Hamiltonians at null infinity
Authors: Ashtekar Abhay , Winicour Jeffrey
Published: March 2003

The relation between the linkage and the symplectic approaches to conserved quantities associated with the Bondi–Metzner–Sachs groups in general relativity is examined.