bluuebunny/crossref_metadata_2025 huggingface dataset:
The accidental degeneracy problem in nonrelativistic quantum mechanics
Authors: Khare Avinash
Published: March 2003

I show that the class of potentials given by V(r)=Ar 2d−2 −Br d−2 possesses partial accidental degeneracy given by En1,l2 =En2,l1 in case d=(l2−l1)/(n2−n1), B=[l+dn+(1−d)/2](2A/μ)1/2. It is further shown that, for a given potential, as the number of dimensions change, the accidental degeneracy pattern also changes except when d=1 and 2. Using these results, it is then shown that for the bottom quark-antiquark (bb̄) bound system, most likely E3S <E1F <E2D. Finally I also make some conjectures about the ordering of levels for a wide class of potentials.
Quasisteady arterial blood flow
Authors: Gordon Paul
Published: March 2003

Fluid flow through a bifurcating system of elastic tubes is modeled with the inviscid compressible time-dependent equations of fluid flow. Because of the physical scale of the problem (the length of the tube is large relative to its diameter), quasisteady analysis can be applied to the system of hyperbolic first order partial differential equations. Several simplified models are thereby obtained. Although similar in some respects to the usual incompressible models, the quasisteady models are seen to be significantly different. For example, the sound speed of the fluid remains an important parameter in the boundary condition. Numerical solutions are obtained for various problems. Results are presented for the one-layer problem, which was studied in some depth, and a three-layer problem, in which the layers are connected by bifurcation boundary conditions. The solutions are shown to be physically reasonable. Of special interest is the clear display of the mechanism in the model by which the elastic wall converts the pulsatile flow to a much more continuous outflow.
Nonlinear periodic waves in a self-gravitating fluid
Authors: Ray Dipankar
Published: March 2003

Liang has obtained equations for nonlinear plane waves in a Jeans universe. While Liang has studied the equation for a specific equation of state, this paper makes a general study. Among other things it is shown that only a subsonic propagation is possible.
Internal labels of degenerate representations
Authors: Seligman T. H. , Sharp R. T.
Published: March 2003

An expression for the number of internal labels of degenerate irreducible representations of compact semisimple Lie groups is given in the same spirit as Racah’s formula for the nondegenerate case.
Remarks on canonical transformations in phase-space path integrals
Authors: Gerry Christopher C.
Published: March 2003

We study canonical transformations in phase-space path integrals in the Schrödinger representation. Using the example of a contact transformation implemented in each short-time propagator via the midpoint method, we show that the ‘‘measure’’ (dpN/2πℏ) ∏Nj=1 [dpjdqj/(2πℏ)], apart from the unpaired dpN, cannot be considered as a product of Liouville measures.
A recurrence relation for the phase shifts of exponential and Yukawa potentials
Authors: Sidharth B. G.
Published: March 2003

Using the Born approximation for high energies, we deduce a recurrence relation for the higher order phase shifts of Yukawa and exponential potentials and their superpositions. Thence a formula for the total cross section is deduced. It is shown that these formulae are particularly useful when the energy is very high. Next, using the low energy technique of expansion in powers of the energy, we deduce an asymptotic formula when l is large, for δl+1/δl. The remarkable thing is that the recurrence relation is identical to the asymptotic formula. It is verified that the formulae for the phase shifts give satisfactory results, which are better than the Born approximation, from l=1 onwards, for scattering by helium and hydrogen atoms, while the formula for the total cross section gives better results than an improved variational technique or the Born approximation.
Quantum virial coefficients as cumulants of imaginary time-ordered Mayer diagrams
Authors: Royer Antoine
Published: March 2003

The virial coefficients for a quantum gas (including quantum statistics) are expressed as sums of cumulants of connected (generalized) Mayer diagrams, the cumulants being built on the irreducible blocks of the diagrams. The Mayer diagrams are defined for the quantum case in terms of imaginary time-ordered exponentials, the quantum statistics being incorporated in the guise of multiparticle interactions. In order to extend Mayer diagrams to multiparticle interactions, we utilize terminology and methods from the theory of hypergraphs. The virial coefficients naturally separate into a quantum Boltzmann gas contribution, an ideal quantum gas contribution, and a final term expressing correlations between dynamics and statistics. In the classical limit, connected Mayer diagrams factorize into their irreducible blocks; the cumulants over irreducible blocks then vanish (by a basic property of cumulants), except for diagrams which are themselves irreducible, whence the classical result of Mayer (extended to multiparticle interactions). In the quantum case, the imaginary time ordering prevents the factorization into irreducible blocks by time entangling them. As a further illustration of the use of hypergraph-cumulant methods, we directly deduce the expressions of the virial coefficients in terms of Ursell–Kahn–Uhlenbeck cluster functions (the ideal quantum gas contribution naturally appears in that form).
Group-theoretical analysis of the sine-Gordon equation as a relativistic dynamical system
Authors: Alonso L. Martínez
Published: March 2003

The inverse scattering transform method is used in order to achieve a group-theoretical characterization of the sine-Gordon equation considered as a relativistic dynamical system. The action of the Poincaré group is formulated in terms of scattering data variables and the three basic components of the sine-Gordon field, namely, solitons, breathers and radiation are identified with simple canonical realizations of the Poincaré group. In particular, the nonlinear flow associated with the one-parameter group of pure Lorentz transformations is integrated by means of the inverse scattering transform method.
A non-Machian solution in Brans–Dicke theory
Authors: Chakraborty S. K.
Published: March 2003

A solution of the vacuum field equations of the Brans–Dicke theory of gravitation admitting a particular group of motions is found out. The solution is of interest because it is supposed to be at variance with Machian ideas of inertia.
A simplified derivation of the Geroch group in two-dimensional reduced gravity
Authors: Wu Yong-Shi , Ge Mo-Lin
Published: March 2003

By generalizing our previous treatment of hidden symmetry in two-dimensional chiral models, a simple and explicit approach is proposed to the Geroch group for the vacuum Einstein equations with the metric tensor depending only on two variables (‘‘two-dimensional reduced gravity’’). An infinite number of infinitesimal transformations for the metric tensor preserving the equations of motion are summarized by an explicit parametric transformation and the commutators among them are calculated in a simple and straightforward way. These transformations and their group structure are further identified to be those of the well-known Geroch group.
Formal state determination
Authors: Ivanović I. D.
Published: March 2003

Following the general results of Park and Band it is shown that any state of a quantal ensemble allowed by the Hilbert space formulation of nonrelativistic quantum mechanics may be determined from the results of measurements, under the assumption that all measurements, those of energy, position, and spin projection, are in accordance with the projection postulate.
Conformal invariance conditions for spinor fields with gauge freedom
Authors: Légaré Martin
Published: March 2003

The global invariance conditions are given for the ( j, j′) spinor fields with gauge freedom invariant under subgroups of C(3,1). We formulate two propositions concerning the nonexistence of nontrivial fields with and without compact gauge freedom and apply them to the maximal noncompact subgroups of C(3,1). We also determine explicitly the most general O(4) and O(2)×O(4) invariant ( j, j′) spinor fields with compact gauge freedom.
Self-dual Yang–Mills fields on Minkowski space–time
Authors: Porter John R.
Published: March 2003

Self-dual Yang–Mills fields are realized as a superposition, but in a nonlinear context, of plane wave fields. The mathematical analysis of such superposition (and the inverse problem of decomposition) is given in terms of connections on the prime spin bundle over Minkowski space–time. This view leads naturally to the twistor construction for such fields given by Ward as well as a CR version of this construction.
Complex scaling of ac Stark Hamiltonians
Authors: Howland James S.
Published: March 2003

For a two-body atom in a temporally periodic, spatially uniform field, it is shown that in an appropriate gauge the essential spectrum of the Floquet Hamiltonian rotates about a certain set of thresholds when subjected to a complex scaling transformation.
Finitely many symmetries of the S-matrix
Authors: Garber Wolf-Dieter
Published: March 2003

S-matrix symmetries are operators that commute with the S-matrix and act additively on incoming n-particle states. For relativistic field theories, the structure of such symmetries is known if they arise from a local, conserved current density. In this note it is shown that the same structural result is obtained if a relativistic field theory with finitely many but possibly nonlocal S-matrix symmetries is considered.
Minimal electromagnetic coupling schemes. I. Symmetries of potentials and gauge transformations
Authors: Beckers J. , Hussin V.
Published: March 2003

Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries inside and outside the symmetry groups of the corresponding free equations. Subsymmetries of relativistic potentials are classified up to conjugacy under the kinematical groups of the associated (constant and uniform) electromagnetic fields. Through invariance conditions on (physical) four-potentials a maximal character of the symmetry is obtained leading to the maximal symmetry groups of the corresponding wave equations with interaction. Usual and compensating gauge transformations are analyzed within the context of such invariance conditions applied to arbitrary electromagnetic fields.
Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups
Authors: Beckers J. , Hussin V.
Published: March 2003

Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries outside the symmetry groups of the corresponding free equations. The Schrader construction of the so-called (relativistic) Maxwell group is reviewed through group extensions of kinematical groups associated with (constant and uniform) electromagnetic fields. The construction of the Galilean (nonrelativistic) Maxwell group is given.
Rayleigh–Taylor instability of a fluid supported against gravity by an oscillating magnetic field
Authors: Chakraborty B. B. , Iyengar H. K. S. , Nayak A. R.
Published: March 2003

Rayleigh–Taylor instability of an incompressible, inviscid, and infinitely conducting heavy fluid supported against gravity by a horizontal and uniform magnetic field is studied. The magnetic field consists of a steady part and an unsteady part, of magnitude varying with time, rotating with a fixed period about a vertical axis. The growth rate of instability of any unstable disturbance is obtained analytically when the magnitude of the unsteady part of the field is small. When the unsteady part of the field is not small, the growth rate is calculated numerically. The analytical as well as the numerical results show that, except in some special cases, the steady and the unsteady field components together have a greater stabilizing influence on the fluid than in the case when the unsteady field is acting alone. A physical explanation of the stabilizing influence of the combined presence of the steady and unsteady field is suggested.
Shift operator techniques for the classification of multipole-phonon states. XI. Properties of mixed type quadratic product operators in R(7)
Authors: Van der Jeugt J. , De Meyer H. E. , Vanden Berghe G.
Published: March 2003

Expressions connecting R(3) scalar and nonscalar product operators of the type P jl+kOkl and Okl+jP jl are constructed within the group R(7).
Shift operator techniques for the classification of multipole-phonon states. XII. O0l eigenstate and eigenvalue determination in R(7)
Authors: Van der Jeugt J. , Vanden Berghe G. , De Meyer H. E.
Published: March 2003

On account of previously derived relations between quadratic shift operator products of the type P jl+kOkl, Okl+jP jl, and Okl+jO jl in the group R(7), part of the eigenvalue spectrum of the scalar shift operator O0l is derived in closed form. The corresponding eigenstates which are closely related to the octupole-phonon state vectors are defined in terms of angular momentum lowering shift operator actions upon the maximum angular momentum state. In the case of l-degenerate states the relation between the previously constructed P0l eigenstates and the derived O0l eigenstates is discussed. A short comment on a numerical method for O0l eigenvalue determination is included.
Restricted multiple three-wave interactions: Integrable cases of this system and other related systems
Authors: Menyuk C. R. , Chen H. H. , Lee Y. C.
Published: March 2003

Restricted multiple three-wave interactions, in which a set of wave triads interact through one shared wave, are discussed. It is shown that this system is integrable when all triads have equal coupling coefficients regardless of the frequency mismatches. This system is then used as a starting point from which to determine integrable cases of a more general class of three-wave interactions.
Time evolution kernels: uniform asymptotic expansions
Authors: Osborn T. A. , Fujiwara Y.
Published: March 2003

For a wide class of self-adjoint Schrödinger Hamiltonians, a detailed description of the time evolution kernel is obtained. In a setting of a d-dimensional Euclidean space without boundaries, the Schrödinger Hamiltonian H is the sum of the negative Laplacian plus a real-valued local potential v(x). The class of potentials studied is the family of bounded and continuous functions that are formed from the Fourier transforms of complex bounded measures. These potentials are suitable for the N-body problem, since they do not necessarily decrease as ‖x‖→∞. An asymptotic expansion in the complex parameter z, around z=0, is derived for the family of kernels Uz(x,y) corresponding to the analytic semigroup {e−zH:Re z>0}, which is uniform in the coordinate variables x and y. The asymptotic expansion has a simple semiclassical interpretation. Furthermore, an explicit bound for the remainder term in the asymptotic expansion is found. The expansion and the remainder term bound continue to the time axis boundary z=it/ℏ (t≠0) of the analytic semigroup domain.
Time evolution of the Wigner function
Authors: Soto-Eguibar Francisco , Claverie Pierre
Published: March 2003

In this paper we give a partial answer to the problem: When does an initially non-negative Wigner function remain non-negative under the effect of the time evolution? We show that, for pure states, this is the case for linear systems only; to prove this we use the fact that the Wigner function is non-negative if and only if the wavefunction is Gaussian. We also prove that the Green’s solution of the evolution equation of the Wigner function, which in the framework of probability theory corresponds to the conditional probability density, takes on negative values. We utilize a theorem, about moments, borrowed from Pawula. We conclude that the Wigner phase-space formulation of quantum mechanics cannot receive a genuine probabilistic interpretation.
A probabilistic formulation of quantum theory. III
Authors: Wenning Thomas , Bach Alexander
Published: March 2003

A representation of the expectation value of quantum mechanics, which recently has been set up for normal states, is generalized to singular states. It is shown that states can be represented by finitely additive measures on the state space, which are σ-additive if and only if the states are normal.
Nonlinear time-dependent anharmonic oscillator: Asymptotic behavior and connected invariants
Authors: Besnard D. , Burgan J. R. , Munier A. , Feix M. R. , Fijalkow E.
Published: March 2003

The motion of a particle in a potential decreasing with time as ‖X‖n is considered. Different time and space rescaling are considered in order to obtain the asymptotic solutions. The validity of adiabatic invariants is discussed. The classical critical case corresponds to the obtainment of self-similar solutions for the quantum problem.
Complex-potential description of the damped harmonic oscillator
Authors: Exner Pavel
Published: March 2003

The multidimensional damped harmonic oscillator is treated by means of a non-self-adjoint Hamiltonian with complex potential. The propagator referring to the evolution semigroup is evaluated from the Lie–Trotter formula. The one-dimensional case is discussed in detail with the following results: (a) the nondamped limit gives the correct propagator including the Maslov phase factor, (b) for some initial conditions, the classical limit of the solution can differ from the behavior of the classical damped oscillator, the difference being negligible in the case of weak damping, and (c) the point spectrum of the considered pseudo-Hamiltonian is found.
The unitarity relations for the off-shell Coulomb T matrix for all partial waves
Authors: van Haeringen H.
Published: March 2003

By employing a recently obtained expression for the partial-wave projection of the off-shell Coulomb T matrix for all l, we prove that the unitarity relations for the Coulomb T matrix hold provided that they are properly modified with the help of Coulombian asymptotic states.
Existence and uniqueness of bound-state eigenvectors for some channel coupling Hamiltonians
Authors: Evans J. W.
Published: March 2003

For the three-particle, two-cluster, 2×2 channel coupling Hamiltonians used, e.g., in H+2 and He bound-state calculations, we demonstrate that typically there exist unique eigenvectors for all bound states. This result also holds, with some technical assumptions on the potentials, for the corresponding 3×3 case provided there are no spurious eigenvectors with bound-state eigenvalues. The proofs use the analogous results for the corresponding Faddeev-type Hamiltonians together with spurious multiplier relationships.
Compatibility of rigid motions with the relativistic incompressibility condition
Authors: Del Olmo V. , Olivert J.
Published: March 2003

The compatibility of the hypoelastic-Synge (isotropic case) and hypoelastic-Carter and Quintana (fully isotropic case) almost-thermodynamic material schemes with the relativistic incompressibility condition, given by Ferrando and Olivert, is analyzed. The behavior of those schemes in Born-rigid motion is also studied and an additional stipulation is joined to the Born rigidity concept. This requisite leads to the vanishing of the relativistic stress tensor spatial variation and, in hypoelastic-Carter and Quintana and hypoelastic-Maugin almost-thermodynamic material schemes, leads to the absence of mechanical power originated by internal rotation. The rigidity definition that is proposed remains valid for more general almost-thermodynamic material schemes, as far as the compatibility with the incompressibility condition quoted above is concerned.
Low-energy sum rules for two-particle scattering
Authors: Bollé D. , Wilk S. F. J.
Published: March 2003

We consider the low-energy expansion of the operators describing a two-particle scattering system and derive recursion relations for the expansion coefficients. The particles of the system are allowed to interact via general (not necessarily spherically symmetric) potentials and can also form zero-energy bound states and/or resonances. Using these expansions, we prove low-energy sum rules for such a system. They relate the negative-energy moments of the trace of the resolvent difference to the bound-state eigenvalues. As an application, we first discuss the low-energy expansion of the two-body total cross section. In particular, we derive a closed expression for the expansion coefficients. We also find that there is always a finite characteristic length in the problem, even in the presence of zero-energy resonances. Secondly, we study the low-temperature behavior of the second virial coefficient.
Some exact solutions of Einstein–Dirac–Maxwell zero mass scalar equations
Authors: Krori K. D. , Bhattacharya R. , Nandy D.
Published: March 2003

In this paper, some exact solutions of Einstein–Dirac–Maxwell zero mass scalar field equations are given.
On spacelike congruences in general relativity
Authors: Tsamparlis M. , Mason D. P.
Published: March 2003

The theory of spacelike congruences in general relativity is briefly reviewed and the physical interpretation of the rotation tensor ℛab, the expansion ℰ, and the shear tensor 𝒮ab, of the curves is discussed. It is proved that if the unit tangent vector to any curve of the congruence is everywhere orthogonal to the 4-velocity field ua of a self-gravitating fluid, then observers comoving with the fluid can be employed along a curve of the congruence if and only if the curves are material curves in the fluid. A congruence of vortex lines is studied in detail. Starting from the Ricci identity for ua and using Einstein’s equations, general expressions in terms of the kinematic quantities and fluid variables are derived for ℛab, 𝒞, and 𝒮ab for a vortex congruence. It is found that ℰ and 𝒮ab depend explicitly on the gravitational field only through the magnetic part of the Weyl tensor, and ℛab only through a term proportional to the total energy flux qa derived from Einstein’s equations. With the aid of Maxwell’s equations, properties of congruences of magnetic field lines, electric field lines, and a certain combination of vortex and magnetic field lines are determined. For a congruence of magnetic field lines in an electrically conducting fluid and assuming the magnetohydrodynamic approximation of vanishing electric field, it is proved that for a comoving observer, ℛab=0 if and only if the conduction current in the fluid is orthogonal to the magnetic field. The propagation equations for ℛab, ℰ, and 𝒮ab along a curve of a spacelike congruence are considered. These equations are developed in full for the special case of a congruence of material curves in a fluid. The divergence, or constraint, equation for the rotation vector is also derived. Where appropriate, corresponding results in Newtonian gravitation theory are given for comparison.
Generalized parastatistics and internal symmetry
Authors: Levine R. Y. , Tomozawa Y.
Published: March 2003

We exhibit generalized parastatistical double commutation relations which allow a solution less restrictive than Green’s ansatz. This leads to local interaction terms in the Lagrangian consistent with an internal symmetry among Green indices. The generalized commutation relations are covariant under this symmetry transformation rather than invariant. The formulation may be applicable to the generation problem as well as supersymmetric model building.
On systems of local operators and the duality condition
Authors: Wichmann Eyvind H.
Published: March 2003

Systems of von Neumann algebras of local operators are considered, and a particular procedure for the construction of such a system from any given set of intrinsically local operators is described. The condition of duality is discussed with particular emphasis on a special form of this condition which appears in previous work by Bisognano and Wichmann. Subsystems generated by any set of local operators in an original irreducible system of local operators are considered. Some properties of the irreducible vacuum representation of such a subsystem are derived assuming the special form of the duality condition for the original system. It is shown that this special condition also holds for the subsystem. It is furthermore shown that weak additivity holds for the reduced system if it holds for the original system.
Some Yang–Mills fields constructed from Maxwell fields
Authors: Hogan P. A.
Published: March 2003

We show that the natural connections on the Hopf bundles S2n+1 →CPn (n≥1) satisfy stronger conditions than Maxwell’s equations. These conditions imply that the natural connections on the U(n) Stiefel bundles SU(n+1)→CPn satisfy the Yang–Mills equations. The use of projector-valued fields enables us to pass from the Hopf to the Stiefel bundles in a natural way.
A Hamiltonian–Lagrangian system of vortex boundary curves
Authors: Hebert D. J.
Published: March 2003

The equations of motion for the boundary of a region of constant vorticity in an inviscid, incompressible fluid are expressed as an infinite dimensional Hamiltonian system and as a Lagrangian system based upon a variational principle. In this formulation the m-fold symmetric, stationary, steady, rotating vortices are analogous to the travelling cnoidal waves in the well-known KdV system.
Splines and the Galerkin method for solving the integral equations of scattering theory
Authors: Brannigan M. , Eyre D.
Published: March 2003

This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado–Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.
Versal deformations of elements of classical Jordan algebras
Authors: Patera J. , Rousseau C.
Published: March 2003

Every involution α defining, by α(X)=−X, the elements of one of the classical Lie algebras o(n, C) and sp(2n, C) over C, and o(p,q), sp(2n,R), u(p,q),o*(2n), and sp(2p,2q) over R, also defines α-symmetric matrices Y=α(Y) spanning the classical Jordan algebras. The paper contains an explicit description of all perturbations of α-symmetric matrices, considered up to equivalence under the action of the corresponding classical Lie group. Such exhaustive perturbations are called versal deformations.
The fundamental invariants of inhomogeneous classical groups
Authors: Perroud M.
Published: March 2003

The Casimir operators of the following groups are explicitly constructed :Rn⧠Gl(n,R), Rn⧠Sl(n,R), Rn⧠O(p,q),Cn⧠U(p,q),R2n⧠Sp(n,R), Cn⧠Gl(n,C),Cn⧠Sl(n,C), Cn⧠O(n,C), C2n⧠Sp(n,C), Hn⧠U*(2n), Hn⧠SU*(2n), Hn⧠O*(2n), Hn⧠Sp( p,q), and R⧠(R2n⧠Sp(n,R)). The method is based on a particular fiber bundle structure of the generic orbits generated by the co-adjoint representation of a semidirect product.
Representation matrices for U(4)
Authors: Balster G. J. , van Roosmalen O. S. , Dieperink A. E. L.
Published: March 2003

We propose an algorithm for the numerical calculation of matrix elements of general U(4) group elements, applicable to large totally symmetric representations of U(4). A possible generalization to the U(6) case is pointed out.
Exact solution of a nonlinear Langevin equation with applications to photoelectron counting and noise-induced instability
Authors: Wódkiewicz K. , Zubairy M. S.
Published: March 2003

A stochastic differential equation of the Langevin type involving a linear and a quadratic noise is considered and an exact solution for the stochastic average of this equation is obtained. This solution is employed to calculate the effect of amplitude fluctuations of an electromagnetic field on the photoelectron counting, and an explicit expression is obtained for the photon counting probability. Finally, the steady state limit is studied and the possibility of an instability induced by the noise is discussed.
Conformal geometry of flows in n dimensions
Authors: Robinson Ivor , Trautman Andrzej
Published: March 2003

Flows generated by smooth vector fields are considered from the point of view of conformal geometry. A flow is defined to be conformally geodesic if it preserves the distribution of vector spaces orthogonal to the lines of the flow. It is shear-free if, moreover, it preserves the conformal structure on these vector spaces. Differential equations characterizing such flows are derived for the general case of an n-dimensional conformal space of arbitrary signature. In the special case of null flows in spacetime, one obtains a refined version of the theorem connecting null solutions of Maxwell’s equations with null flows that are geodesic and shear-free.
On the Radon–Nikodym property for σ-classes
Authors: Navara Mirko , Pták Pavel
Published: March 2003

We show that a σ-class with the Radon–Nikodym property need not be a Boolean σ-algebra. This disproves the conjecture of Gudder and Zerbe.
Compatibility of the uncorrelated joint distribution with the classical limit
Authors: Sutherland Roderick I.
Published: March 2003

It is shown that the uncorrelated joint distribution, when adopted for quantum mechanics, is not (despite initial appearances to the contrary) in conflict with the known correlations between position and momentum in the classical limit. It is therefore not excluded on these grounds as a possible joint distribution expression for quantum mechanics.
A rigged Hilbert space of Hardy-class functions: Applications to resonances
Authors: Gadella M.
Published: March 2003

The explicit construction of a dense subspace Φ of square integrable functions on the positive half of the real line is given. This space Φ has the properties that: (1) it is endowed with a metrizable nuclear topology, (2) it is stable under multiplication by x, and (3) the functions in Φ have suitable analytical continuation to a half plane. The space Φ* of functions which are conjugate to elements of Φ is also considered. Then the triplets Φ⊆ ℒ2 (0,∞)⊆Φ′ and Φ*⊆ ℒ2 (0,∞)⊆Φ*′ are used to give a description of resonances.
Operator theory on the WKB method and Bremmer series
Authors: Dudley David , Wang Alan P.
Published: March 2003

The well-known WKB method and Bremmer series in mathematical physics have various modifications and applications. Basically, they are all limited to the finite-dimensional case. Such methods have been extended to the infinite-dimensional case in this paper, i.e., operators on a general normed linear space. This enables us to apply the methods to solve the problem of transport of radiation through a layer of cloud. The derivation is based on input-output states and linear operators. Some elementary properties are exploited, along with physical interpretations. The convergence of the series is established. An example is given to demonstrate the methods and the rate of convergence.
On the dynamical symmetry of the Morse potential problem
Authors: Sun Chia-Chung , Zeng Zong-Hao
Published: March 2003

As is well known, the vibration–rotational Schrödinger equation with Morse potential for diatomic molecules has been solved approximately. In this article, a dynamical symmetry analysis of the same Schrödinger equation is performed to give the symmetries described by two kinds of groups, SO(2,1) and H4×SO(3,2).
Strong approximation of wave operators for short range and Coulomb interactions
Authors: Kröger Helmut
Published: March 2003

For the two-body system with short range potentials the wave operators are shown to be strongly approximatable by exponentials of bounded or even finite-rank operators, which allow the calculation by expansion in a power series or even by some finite-dimensional matrix algebra. It is based on a bounded strong approximation of the kinetic energy Hamiltonian. For the Coulomb potential the same kind of result is obtained for the Dollard modified wave operators. A generalization for the N-body system is sketched.
Continuity of wave and scattering operators with respect to interactions
Authors: Brüning E. , Gesztesy F.
Published: March 2003

Using time-dependent as well as time-independent methods we establish strong continuity of wave and scattering operators within the two Hilbert space formulation of scattering theory. Our applications to potential scattering include continuity of nonforward total cross sections, scattering amplitudes, and operators for Coulomb-type interactions in R3 and continuity of wave operators for strongly singular potentials in Rn, n≥3.
On the optical approximation in two-channel systems
Authors: Exner P. , Úlehla I.
Published: March 2003

The optical approximation for two-channel quantum mechanical systems is treated within Kato theory of smooth perturbations. Concerning the difference between the optical and exact scattering matrices, the theorem deduced recently by Davies is generalized: essentially the same assertion is proved without unphysical neglection of the ‘‘diagonal’’ interaction terms.
The Fierz identities—A passage between spinors and tensors
Authors: Takahashi Yasushi
Published: March 2003

All possible Fierz identities among 16 elements in the Dirac algebra have been obtained. These relations impose various constraint conditions on Hermitian and non-Hermitian bilinear currents. Independent relations are sought out from the highly redundant system of constraint conditions. Relations between derivatives of a spinor and tensor currents are also obtained.
Superoperator perturbation theory for propagators
Authors: Weiner Brian
Published: March 2003

A well-defined superoperator perturbation theory for propagators is developed, based on equivalence classes of operators, which avoids the ambiguity of approaches based on a degenerate inner product. The Van Vleck formalism provides a natural tool for such a theory when self-consistent propagator approximations are chosen as zeroth-order approximations.
Scattering theory for the dilation group. I. Simple quantum mechanical scattering
Authors: Corbett J. V.
Published: March 2003

A theory of scattering based on the dilation group is developed for quantum mechanical one-particle systems. A scattering operator is defined that agrees with the usual scattering operator, whenever the usual wave operators exist and are asymptotically complete.
An exactly solvable quantum field theory in three dimensions
Authors: Sudarshan E. C. G. , Tata Xerxes
Published: March 2003

We construct a quantum field theoretic model in three space dimensions and show that its spectrum can be exactly calculated. We also show that all the eigenvectors of the Hamiltonian can be obtained by a recursive procedure.
Remarks on the Tomimatsu–Sato metrics
Authors: Hoenselaers Cornelius , Ernst Frederick J.
Published: March 2003

After introducing a new way of writing the Tomimatsu–Sato solutions of Einstein’s field equations, we consider the geometry in the neighborhood of the ‘‘poles.’’ We also show that nonequatorial timelike and null geodesics can reach none of the ring singularities.
Null cone computation of gravitational radiation
Authors: Isaacson R. A. , Welling J. S. , Winicour J.
Published: March 2003

The production of gravitational waves is explored, both analytically and numerically, using a null cone formulation of axially symmetric gravitational and matter fields. The coupled field equations are written in an integral form, on a single conformally compactified patch, which is well suited for numerical computation. Some analytic and numerical solutions of the initial value problem are given. The total mass and radiation flux is studied in detail for a special class of collapsing dust configurations.
Casimir invariants, characteristic identities, and Young diagrams for color algebras and superalgebras
Authors: Green H. S. , Jarvis P. D.
Published: March 2003

The generalized commutation relations satisfied by generators of the general linear, special linear, and orthosymplectic color (super) algebras are presented in matrix form. Tensor operators, including Casimir invariants, are constructed in the enveloping algebra. For the general, special linear and orthosymplectic cases, eigenvalues of the quadratic and higher Casimir invariants are given in terms of the highest-weight vector. Correspondingly, characteristic polynomial identities, satisfied by the matrix of generators, are obtained in factorized form. Classes of finite-dimensional representations are identified using Young diagram techniques, and dimension, branching, and product rules for these are given. Finally, the connection between color (super) algebras and generalized particle statistics is elucidated.
Inequalities and local uncertainty principles
Authors: Price John F.
Published: March 2003

Inequalities for Fourier transforms are developed which describe local uncertainty principles in the sense that if the uncertainty of momentum is small, then so is the probability of being localized at any point. They give estimates for essentially all states and lead to lower bounds for Hamiltonians.
Superposition rules for nonlinear coupled first-order differential equations
Authors: Strobel George L.
Published: March 2003

Pairs of coupled nonlinear differential equations of the polynomial type have been studied. No higher powers than quadratic were considered. Lie’s theorem provides a superposition rule exists if certain operators generate a finite-dimensional Lie algebra. The Lie algebras possible were divided into twenty categories. For each case the general form of the coupled differential equations is obtained. The coupled differential equations are then separated where possible. Solutions are obtained expressed in terms of a finite number of particular solutions.
Nonlinear evolution equations and nonabelian prolongations
Authors: Leo M. , Leo R. A. , Soliani G. , Solombrino L. , Martina L.
Published: March 2003

A systematic analysis of the class of nonlinear evolution equations ut +uxxx +φ(u, ux)=0 is carried out within the Estabrook–Wahlquist prolongation scheme.
Higgs fields as Bargmann–Wigner fields and classical symmetry breaking
Authors: do Amaral A. F. Furtado , Doria F. A. , Gleiser M.
Published: March 2003

We show that Higgs fields can be written as Bargmann–Wigner–Teitler spin-0 fields. When they interact with a gauge field, the usual inconsistency in the interaction equations is interpreted as Nambu’s algebraic condition for nontrivial topological properties in the coupled system.
Rigorous theory of spectra and radiation for a model in quantum electrodynamics
Authors: Arai Asao
Published: March 2003

We study rigorously the problem of the lamb shift and the spontaneous emission of light in a framework of nonrelativistic quantum electrodynamics by using an exactly soluble model of a harmonic oscillator atom interacting with a quantized electromagnetic field. We show that, under the perturbation of the electromagnetic field, all the point spectra corresponding to the excited states of the unperturbed atom disappear. This means that the ‘‘energy level shifts’’ (Lamb shifts) of the excited states of the atom cannot be described simply in terms of shifts of point spectra. Then, we give a rigorous mathematical meaning to both formal perturbation theories for the ‘‘energy level shifts’’ and for the transitions of the excited states due to the spontaneous emission of light, showing that the ‘‘energy level shifts’’ and the ‘‘decay probabilities’’ of the excited states of the atom are characterized in terms of the resonance pole of the S-matrix for the photon scattering by the atom. We also discuss broken symmetry aspects and infinite mass-renormalization of the model.
Exact dynamics of a model for a three-level quantum system interacting with a continuous spectrum
Authors: Davidson Russell , Kozak John J.
Published: March 2003

Previous work of the authors on a three-level quantum system is extended to allow the radiation field in interaction with the system to have a continuous spectrum of possible frequencies. The limiting procedure involved in the passage from discrete to continuous spectra is complicated by the need to express sums over different discrete spectra as integrals with well-behaved limits. Exact expressions are found, for a spontaneous emission problem, for the time evolution of the probabilities that the system be in (each) one of its three states and representative calculations of these probabilities are presented. The emergence of irreversible behavior upon constructing the thermodynamic limit of the problem is plainly seen and this demonstration permits for the first time a discussion of the relative effectiveness of competing decay channels in three-level quantum systems without imposing any ad hoc assumptions (such as exponential decay). Rather, the actual form of the decay emerges as a consequence of the structure and parameters of the Hamiltonian defining the model, and hence one can examine the variety of circumstances in which the evolution can reasonably be described as exponential. The results obtained should be of great use in clarifying certain outstanding conceptual problems in radiation physics, particularly those which deal with the universality of exponential decay in three- (and two-) level quantum systems in interaction with a radiation field and the conditions under which nonexponential or even nonergodic behavior can emerge in such dissipative quantum systems.
Stationary wave envelopes in nonlinear optics
Authors: Chanda Pranab Krishna , Ray Dipankar
Published: March 2003

Small has given a set of equations for stationary electromagnetic wave envelopes in a cubically nonlinear two-dimensional medium and has obtained some particular solutions. These solutions are generalized. Some solutions of the Ginzburg–Pitaevski equation for superfluid are obtained as a by-product.
Cartan structures on Galilean manifolds: The chronoprojective geometry
Authors: Burdet G. , Duval C. , Perrin M.
Published: March 2003

A new geometry is constructed over Galilean manifolds expressing the compatibility requirement between the conformal equivalence notion of two Galilean structures and the projective equivalence notion of two affine connections. It is shown that it is the very geometry of the Newtonian cosmology (chronoprojective flatness is equivalent to isotropy of Newtonian cosmological models); moreover, it also explains various ‘‘accidental’’ symmetries in classical mechanics.
Unification of Ernst-equation Bäcklund transformations using a modified Wahlquist–Estabrook technique
Authors: Harrison B. Kent
Published: March 2003

The three known Bäcklund transformations for the Ernst equation are derived using a modification of the Wahlquist–Estabrook prolongation procedure. The modification requires that the equation to be studied be cast into a set of differential forms and their exterior derivatives, such that all coefficients are constant (a ‘‘CC ideal’’). Analysis of the resulting equations produces 16 solutions composed of the three basic transformations combined with identity and other essentially trivial transformations. The group structure of the transformations is discussed. A Bäcklund transformation (already known) for the Ernst–Maxwell equations can be found by the same method. Promising generalizations are mentioned.
On apparent horizons and the Schwarzschild surface for a uniform fluid sphere in general relativity
Authors: Knutsen Henning
Published: March 2003

The time history of the marginally trapped surfaces, i.e., the apparent horizons for a spherically symmetric nonstatic fluid of uniform density are studied. Generally it is found that apparent horizons may or may not exist dependent upon the choice of arbitrary functions of integration. However, it is shown in this paper that if the metric is conformally flat or if the circumference of the sphere is an increasing function of a radial coordinate, apparent horizons exist if and only if the surface is inside the Schwarzschild surface. Then there exist in fact at least two horizons: The absolute Schwarzschild surface and an apparent horizon in the interior of the fluid matter.
Symmetries of the nontwisting type-N solutions with cosmological constant
Authors: Salazar I. Humberto , García D. Alberto , Plebański Jerzy F.
Published: March 2003

The conformal, homothetic, and isometric symmetries of all nontwisting type-N solutions are established. All solutions with λ allow at most the existence of two Killing vectors. All vacuum solutions, except the Robinson metric, permit maximally the existence of two (isometric and homothetic) symmetries. The Robinson solutions are the only ones which allow conformal symmetries.
Current responses of first and second order in a collisionless plasma. III. Three-wave interaction in periodic plasmas
Authors: Larsson Jonas
Published: March 2003

Three-wave interaction in a possibly strongly inhomogeneous plasma was considered in Paper II. These results are now generalized in order to treat also time-dependent periodic systems. The coupled mode equations as given in this paper are applicable to a very large class of unperturbed systems including those in Paper II and plasmas with self-consistent or in external oscillating field and also plasmas with some crystal symmetry in space-time. In the particular case when the relativistic Vlasov equation is used to describe the plasma we give symmetric expressions for the coupling coefficients such that the Manley–Rowe relations follow if wave–particle interaction is neglected.
On a new hierarchy of Hamiltonian soliton equations
Authors: Boiti M. , Laddomada C. , Pempinelli F. , Tu G. Z.
Published: March 2003

A method is suggested for studying the Hamiltonian structure of the nonlinear partial differential equations that can be solved by the use of the spectral transform (soliton equations). The method is applied to a new hierarchy of N+1 coupled partial differential equations related to a Schrödinger-like spectral problem. It is shown that these soliton equations are integrable Hamiltonian equations with commuting flows. For N=1 and N=2 a Miura-like transformation is computed and the corresponding modified equations are explicitly given.
Maximal abelian subalgebras of real and complex symplectic Lie algebras
Authors: Patera J. , Winternitz P. , Zassenhaus H.
Published: March 2003

We provide guidelines for classifying maximal abelian subalgebras (MASA’s) of the symplectic Lie algebras sp(2n, R) and sp(2n, C) into conjugacy classes under the Lie groups Sp(2n, R) and Sp(2n, C), respectively. The task of classifying all MASA’s is reduced to the classification of orthogonally indecomposable (OID) MASA’s. Two types of orthogonally indecomposable MASA’s of sp(2n, C) exist: 1. Indecomposable maximal abelian nilpotent subalgebras (MANS’s). 2. Decomposable MASA’s [their classification reduces to a classification of MANS’s of sl(n, C)]. Four types of orthogonally indecomposable MASA’s of sp(2n, R) exist: 1. Absolutely indecomposable MASA’s (MANS’s). 2. Relatively indecomposable MASA’s [their classification reduces to a classification of MANS’s of su( p, q) for p+q=n]. 3. Decomposable absolutely OID MASA’s [involving MANS’s of sl(n,R)]. 4. Decomposable relatively OID MASA’s [involving MANS’s of sl(n/2, C), for n even]. Low-dimensional cases of sp(2n, F) (n=1, 2, 3, F=R or C) are treated exhaustively. The algebras sp(2, R), sp(4, R), and sp(6, R) have 3, 10, and 30 classes of MASA’s, respectively; sp(2, C), sp(4, C), and sp(6, C) have 2, 5, and 14 classes of MASA’s, respectively. For n≥4 infinitely many classes of MASA’s exist.
On a new class of gradient formulas in the angular momentum theory
Authors: Niukkanen A. W.
Published: March 2003

Recently B. F. Bayman has derived the formula for 𝒴lm(∇)φ(r)𝒴LM(r), where 𝒴lm(r) is a solid spherical harmonic, in terms of the derivatives of the function φ(r) by the scalar parameter r. This result is clarified and essentially generalized for the case of the tensor product {𝒴nl(∇)⊗φ(r)𝒴L(r)}λμ, where 𝒴nlm(∇)=Δn𝒴lm(∇), in this paper. Applications to the Taylor series in the three-dimensional Euclidean space, as well as some other expansions, are discussed briefly.