JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Search Issue | RSS Feeds RSS
Previous Issue Next Issue

Nov 1977

Volume 18, Issue 11, pp. 2087-2240


Free particle systems and their dynamics in de Sitter space

Raymond C. Fabec

J. Math. Phys. 18, 2087 (1977); http://dx.doi.org/10.1063/1.523185 (5 pages) | Cited 1 time

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
A first step in determining all the global projective unitary representations describing free particle systems in imaginary Lobachevsky space is made. Essentially we determine explicitly the global form of any representation describing a free particle of spin j on the group generated by rotations and translations of space–time at time t and time translations. We also discuss whether or not positional observables should be preserved under physical equivalence and determine the effects this has on the representation theory of free particle systems.
Show PACS
02.40.Ma Global differential geometry

A tachyon dust universe

Sushil K. Srivastava

J. Math. Phys. 18, 2092 (1977); http://dx.doi.org/10.1063/1.523186 (5 pages) | Cited 2 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
In the present paper some investigations have been made on the model suggested by Ray for a tachyon dust universe and the results obtained have been compared with the results in the flat Friedmann universe filled with ordinary dust (here called bradyon dust) moving slower than light, by various scientists, on the ground that the role played by time for ordinary matter is played by spatial coordinates for tachyons. The effect of the cosmological constant (Λ) on the expanding tachyon universe also has been discussed here. The tetrad technique has been used as a mathematical tool for handling the problems of gravitational field equations and perturbation of momentum flux.
Show PACS
98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

K matrix for the Woods–Saxon potential

B. Talukdar and M. N. Sinha Ray

J. Math. Phys. 18, 2097 (1977); http://dx.doi.org/10.1063/1.523187 (2 pages) | Cited 1 time

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
The s‐wave part of the off‐shell K matrix elements for the Woods–Saxon potential has been obtained in terms of elementary transcendental functions by using the differential equation approach to off‐shell scattering.
Show PACS
11.80.-m Relativistic scattering theory

Stability, equilibrium and KMS for an infinite classical system

M. Pulvirenti

J. Math. Phys. 18, 2099 (1977); http://dx.doi.org/10.1063/1.523188 (5 pages) | Cited 4 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
The stability condition as a property which characterizes the thermodynamic equilibrium is studied from an abstract point of view. Furthermore, an application of the main result to the case of an infinite classical harmonic system is given.
Show PACS
05.20.Gg Classical ensemble theory

On notions of Markov property

G. O. S. Ekhaguere

J. Math. Phys. 18, 2104 (1977); http://dx.doi.org/10.1063/1.523189 (4 pages) | Cited 1 time

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
We exhibit the logical connection between two mathematically and physically interesting notions of Markov property due to Nelson [J. Funct. Anal. 12, 97 (1973)] and to Wong [Ann. Math. Stat. 40, 1625 (1969)], respectively, in the case of Gaussian generalized stochastic fields.
Show PACS
02.50.Ga Markov processes

Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundaries

James G. Berryman

J. Math. Phys. 18, 2108 (1977); http://dx.doi.org/10.1063/1.523190 (8 pages) | Cited 27 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
A class of quasilinear parabolic equations with fixed boundaries arising in studies of cross‐field diffusion in toroidal multipole plasmas is presented. It is well known that these equations have separable solutions which decay in time. Surprisingly, both octupole and numerical experiments show, in particular cases, that the separable solution evolves from an arbitrary initial distribution of particles. The evolution and stability properties of these solutions are demonstrated in this paper. When the coefficients of the equations are independent of the spatial variable, infinitesimal perturbations decay as the fourth power (or higher) of the separable solution time dependence; the separable solution is therefore stable. When the initial particle distribution has no nulls except at the boundaries, an approximate analysis shows that large perturbations decay exponentially causing the rapid evolution of the separable solution. The analysis allows the asymptotic behavior of the system to be predicted approximately from knowledge of the initial particle distribution.
Show PACS
02.30.Jr Partial differential equations

Global structure of the ’’Kantowski–Sachs’’ cosmological models

C. B. Collins

J. Math. Phys. 18, 2116 (1977); http://dx.doi.org/10.1063/1.523191 (9 pages) | Cited 57 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
A discussion is given of the ’’Kantowski–Sachs’’ cosmological models; these are defined locally as admitting a four‐parameter continuous isometry group which acts on spacelike hypersurfaces, and which possesses a three‐parameter subgroup whose orbits are 2‐surfaces of constant curvature (i.e., the models possess spherical symmetry, combined with a translational symmetry, and can thus be regarded as nonempty analogs of part of the extended Schwarzschild manifold). It is shown that all general relativistic models in which the matter content is a perfect fluid satisfying reasonable energy conditions are geodesically incomplete, both to the past and to the future, and that at each resulting singularity the fluid energy density is infinite. In the case where the fluid obeys a barotropic equation of state (which includes all known exact perfect fluid solutions) the field equations are shown to decouple to form a plane autonomous subsystem. This subsystem is examined using qualitative (Poincaré–Bendixson) theory, and phase–plane diagrams are drawn depicting the behavior of the fluid’s energy density and shear anisotropy in the course of the models’ evolution. Further diagrams depict the conformal structure of these universes, and a table summarizes the asymptotic properties of all physically relevant variables.
Show PACS
98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

A necessary condition for the validity of Huygens’ principle on a curved space–time

Riccardo Goldoni

J. Math. Phys. 18, 2125 (1977); http://dx.doi.org/10.1063/1.523192 (4 pages) | Cited 1 time

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
It is proved that a necessary condition for the validity of Huygens’ principle on a curved space–time V4 is that V4 be an Einstein space. In connection with this result some remarks about the strong and weak formulations of Mach’s principle are also pointed out.
Show PACS
02.40.Ky Riemannian geometries

Perturbation solution of the Percus–Yevick equation for the square‐mound potential

A. Fuliński and C. Jȩdrzejek

J. Math. Phys. 18, 2129 (1977); http://dx.doi.org/10.1063/1.523193 (4 pages) | Cited 2 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
The perturbation solution of the Percus–Yevick equation, based on the known solution for hard‐sphere interactions, is found for the square‐mound potential. The correlation functions are expanded in powers of the parameter α, related to the height of the mound, i.e., describing the deviation of the interactions from the hard‐sphere ones. An algorithm for the calculation of subsequent coefficients is given. Numerical calculations show, however, that the series converges slowly and thus a few terms approximate the whole series with sufficient accuracy for small (but still finite) values of α, i.e., for almost hard‐sphere interactions, only. For mounds high enough the system behaves very similarly to the hard‐sphere system, but it quickly loses its ’’hard’’ characteristics as the mound decreases. This result, in the light of the success of the recent perturbation theory of liquids, seems to suggest that, whereas fairly significant changes of the potential in the outside of the hard core may be treated as small perturbations, even a small change inside the hard core very strongly perturbs the properties of the system.
Show PACS
02.30.Rz Integral equations

Functional equations for extended hadrons

Z. Haba

J. Math. Phys. 18, 2133 (1977); http://dx.doi.org/10.1063/1.523194 (5 pages) | Cited 2 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
We consider the problem of solution of some functional equations occurring in the theory of extended hadrons. By means of stochastic methods solutions of these equations are obtained in the form of a contractive (Markov) semigroup in Hilbert space. Analytic continuation to a unitary group implementing time evolution is performed. The problem of unitary implementability of Lorentz and gauge symmetries, essential for physical interpretation, remains unsolved.
Show PACS
02.30.Sa Functional analysis
02.50.Ey Stochastic processes

Quantum counting processes

M. D. Srinivas

J. Math. Phys. 18, 2138 (1977); http://dx.doi.org/10.1063/1.523195 (8 pages) | Cited 22 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
It is proposed that counting experiments in quantum physics should be analyzed in terms of point processes (QPP) defined in the framework of quantum probability theory. A coincidence approach is developed for a class QPP called the regular QPP. A counting formula is derived which determines completely the counting statistics of a regular QPP by means of a pair of ’’generators.’’
Show PACS
03.65.Ta Foundations of quantum mechanics; measurement theory

The gravitational influence of a beam of light of variable flux

Raymond W. Nackoney

J. Math. Phys. 18, 2146 (1977); http://dx.doi.org/10.1063/1.523196 (7 pages) | Cited 2 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
An exact solution is obtained for the Einstein field equations of a columnated, time varying beam of light. The beam is circular in cross section, infinite in path length, and is considered in the geometrical limit. The beam is described in a retarded time coordinate system. The flux density is dependent on the radial coordinate and on the retarded time. The solution is sufficiently general so as to describe a single pulse of light traveling through a vacuum. It also allows the description of acceleration fields which propagate in the direction of the beam at the speed of light. Geodesics are considered in order to test the interpretation of the solutions and the stability of the time varying beam.
Show PACS
04.20.Jb Exact solutions

Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times

Carlos Moreno

J. Math. Phys. 18, 2153 (1977); http://dx.doi.org/10.1063/1.523197 (9 pages) | Cited 10 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
In stationary space–times Vn×R with compact space‐section manifold without boundary Vn, the Klein–Gordon equation is solved by the one‐parameter group of unitary operators generated by the energy operator i−1T−1 in the Sobolev spaces Hl(Vn) ×Hl−1(Vn). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency‐part solutions defined by means of this kernel are constructed.
Show PACS
03.65.Pm Relativistic wave equations
02.30.Jr Partial differential equations

A note on the range of the applicability of the Ornstein–Zernike theory in the van der Waals model

Marek Napiórkowski

J. Math. Phys. 18, 2162 (1977); http://dx.doi.org/10.1063/1.523182 (4 pages)

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
We show that the condition determining the range of the applicability of the Ornstein–Zernike theory obtained previously by Hemmer for the van der Waals model is too strong. The weaker condition obtained by us is in agreement with the existing results for different physical systems, and it requires the temperature to satisfy the following inequality: (T−Tc)/Tc≫ (γd)6, where γd denotes the ratio of the short‐range part of the potential to the range of the long‐range part and Tc is the critical temperature predicted in the van der Waals model.
Show PACS
64.10.+h General theory of equations of state and phase equilibria
61.20.Gy Theory and models of liquid structure

Generators of infinite direct products of unitary groups

K. Kraus, L. Polley, and G. Reents

J. Math. Phys. 18, 2166 (1977); http://dx.doi.org/10.1063/1.523183 (6 pages) | Cited 5 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
Under suitable conditions, an infinite direct product ⊗nUn(t) of continuous unitary one‐parameter groups Un(t) is again a continuous unitary one‐parameter group. This question is discussed here in terms of the generators An of Un(t). It is shown that the generator A of ⊗nUn(t) has a total set of product vectors in its domain of definition. As examples, the particle number, energy–momentum, and angular momentum operators in non‐Fock direct product representations of free fields are investigated. The spectra of these operators are determined.
Show PACS
03.65.Fd Algebraic methods
02.20.Qs General properties, structure, and representation of Lie groups

Sequences of transformations for particle‐field Hamiltonians

Eugene P. Gross

J. Math. Phys. 18, 2172 (1977); http://dx.doi.org/10.1063/1.523184 (5 pages)

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
The nonrelativistic Hamiltonian for a particle interacting with a scalar field is studied by a method that involves a product of unitary transforms. We use intermediate coupling transforms for finite particle momenta to treat the interaction with oscillators with a range of wave vectors. Elimination of the oscillators in the range leads to a new Hamiltonian of the identical operator structure but with a modified interaction and mass. We show that with any finite number of divisions the self energy is always lower than the intermediate coupling result. In the limit of infinitely many divisions differential equations are derived for the interaction and effective mass as a function of the smallest wave vector of the oscillators that have been removed.
Show PACS
11.10.Ef Lagrangian and Hamiltonian approach

Magnetic monopoles in SU(4) gauge theories

Y. Brihaye and J. Nuyts

J. Math. Phys. 18, 2177 (1977); http://dx.doi.org/10.1063/1.523198 (14 pages) | Cited 5 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
All spherically symmetric magnetic poles are explictly constructed in SU(4). We show the relevance of the concept of the little group which transforms spherically symmetric solutions among themselves. Unlike the SU(2) and SU(3) situation this little group is not always Abelian in SU(4). On the other hand, it is shown that while the total strength of the pole is always quantized its projection along the Higgs field is sometimes arbitrary. This is also in contrast with the SU(2) and SU(3) cases.
Show PACS
11.15.-q Gauge field theories
14.80.Hv Magnetic monopoles
11.30.-j Symmetry and conservation laws

Stationary gravitational fields of a charged perfect fluid

S. Kloster and A. Das

J. Math. Phys. 18, 2191 (1977); http://dx.doi.org/10.1063/1.523199 (3 pages) | Cited 4 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
Einstein’s field equations which include electromagnetism are investigated when the metric admits a timelike Killing motion and the source is a charged perfect fluid under isometric motion. It is shown that the pressure must necessarily be a function of the electrostatic and gravitational potentials. A class of solutions is found under the following simplifying assumptions: (i) The pressure is a constant, (ii) the Lorentz force vanishes, and (iii) the magnetic and twist potentials are functionally related. In this class the ratio of σ/(ρ+3p) is a constant and this resembles an equilibrium condition. Finally a four‐parameter group (maximal) is supplied which can generate new solutions of this class.
Show PACS
04.20.Jb Exact solutions
04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime

Lee model with 3V particles

Cvavb. Chandra Raju

J. Math. Phys. 18, 2194 (1977); http://dx.doi.org/10.1063/1.523200 (10 pages)

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
The 3V‐particle Lee model is proposed. The NΘ scattering amplitude, the VΘ scattering amplitude and the nΘΘ production amplitude are evaluated. The integral equation in the VΘ sector is solved. The usual deductive method cannot be applied here to solve the integral equation of the VΘ sector. A nondeductive method is applied to solve the integral equation. The solution obtained correctly reduces to the solution of the VΘ integral equation of the ordinary Lee model, whenever any two bare interaction constants in the Hamiltonian are switched off. The two resonances that appear in the NΘ sector, again appear in the VΘ sector at the same energies.
Show PACS
11.90.+t Other topics in general theory of fields and particles (restricted to new topics in section 11)

Fermi–Bose and internal symmetries with universal Clifford algebras

Geoffrey Dixon

J. Math. Phys. 18, 2204 (1977); http://dx.doi.org/10.1063/1.523201 (3 pages) | Cited 1 time

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
Supersymmetry in four‐dimensional space–time is approached from the theory of universal Clifford algebras. The representation produced results in a class of new algebras characterized by an index n which indicates the natural appearance of su(2n) ×u(1) as a subalgebra interacting only with the spinor (or odd) parts of the surrounding Fermi–Bose algebra. Finally, a reformulation of the Dirac equation in this formalism is presented which is not plagued with the empirically untenable problem of a continuous range of eigenvalues.
Show PACS
02.20.Sv Lie algebras of Lie groups
02.10.Ud Linear algebra
02.10.Xm Multilinear algebra

A Lie group framework for soliton equations. I. Path independent case

James Corones, B. L. Markovski, and V. A. Rizov

J. Math. Phys. 18, 2207 (1977); http://dx.doi.org/10.1063/1.523202 (7 pages) | Cited 8 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
A general Lie group theoretic framework for the study of a class of nonlinear partial differential equations is presented. In two space–time dimensions this class includes soliton equations. The approach is applicable in N⩽2 space–time dimensions. Eigenvalue problems and isospectral flows associated with equations have a natural group theoretic interpretation in this framework. A sequence of nonlocal exact 1‐,2‐,...,(N−1) ‐forms are derived in N‐dimensional space–time.
Show PACS
02.30.Jr Partial differential equations
02.20.Qs General properties, structure, and representation of Lie groups

Discrete path approach to linear recursion relations

Adel F. Antippa

J. Math. Phys. 18, 2214 (1977); http://dx.doi.org/10.1063/1.523203 (9 pages) | Cited 11 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
It is shown that the solutions of linear homogeneous recursion relations, with arbitrarily specified boundary conditions, are related, by a mapping, to the totality of discrete paths joining the two ends of an interval and made up of a predetermined set of directed segments. We study the dependence of these solutions on the way the boundary conditions are specified. When the boundary conditions are given as initial conditions, the present approach reduces to the formalism already developed for that specific case, and which is based on the partitions of an interval into classes.
Show PACS
02.30.-f Function theory, analysis

The translation kernel in the n‐dimensional scattering problem

Marcel Coz and Pierre Rochus

J. Math. Phys. 18, 2223 (1977); http://dx.doi.org/10.1063/1.523204 (9 pages) | Cited 3 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
Radial wavefunctions are defined for the n‐dimensional scattering problem (n≳1) with spherical symmetry by conditions of regularity at the origin or by conditions of behavior at infinity. The existence of translation kernels can therefore be discussed in both instances. The problem of representing regular solutions appears to be essentially different from that of representing irregular solutions. The essential difference originates from the type of domain used in the representation: It is bounded in the first case and unbounded in the second. If one can still compare the ranges of validity of the two types of representation when one is dealing with a scalar situation, upon proceeding to a matrix situation, a comparison is no longer possible.
Show PACS
02.30.Rz Integral equations

Translation kernels for velocity dependent interactions

M. Coz and P. Rochus

J. Math. Phys. 18, 2232 (1977); http://dx.doi.org/10.1063/1.523205 (9 pages) | Cited 4 times

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Show Abstract
We reconsider first the representation of solutions defined by a condition at the origin and recognize the difficulty of extending the representation outside simple cases. By eliminating the study of solutions defined at the origin in further studies the translation kernels for velocity dependent interactions are constructed only for solutions defined by their behavior at infinity. Two methods are proposed: They are shown to be equivalent in physical cases and to extend to these physical situations.
Show PACS
11.80.-m Relativistic scattering theory
02.30.Uu Integral transforms
02.30.Vv Operational calculus
02.30.Hq Ordinary differential equations
FREE

Erratum: Higher weights of semisimple Lie algebras

W. Laskar

J. Math. Phys. 18, 2240 (1977); http://dx.doi.org/10.1063/1.523206 (1 page)

Online Publication Date: 26 August 2008

Full Text: | Download PDF

Abstract Unavailable
Show PACS
02.20.Sv Lie algebras of Lie groups
99.10.Cd Errata
Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Completely positive dynamical semigroups of N‐level systems
  2. The Einstein Tensor and Its Generalizations
  3. An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field
  4. Solution of a Three‐Body Problem in One Dimension
Go to AIP Home
Copyright © American Institute of Physics
close