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

Flickr Twitter UniPHY Group iResearch App Facebook

Search Issue | RSS Feeds RSS
Previous Issue Next Issue

Sep 1986

Volume 27, Issue 9, pp. 2217-2446

Page 1 of 2 Pages Next Page | Jump to Page

Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras

J. Beckers, V. Hussin, and P. Winternitz

J. Math. Phys. 27, 2217 (1986); http://dx.doi.org/10.1063/1.526993 (11 pages) | Cited 10 times

Full Text: | Download PDF

Show Abstract
In order to study nonlinear ordinary differential equations with superposition principles, related to the exceptional simple Lie group G2, the complex and real forms of its Lie algebra are examined and their maximal subalgebras are summarized. In particular the parabolic subalgebras of the noncompact real form gNC2(R) are determined. Explicit matrix realizations of the fundamental representation D(1,0) are used and studied in connection with invariant subspaces in a seven‐dimensional (complex or real) vector space. The results are collected in three tables of specific interest for the study of nonlinear differential equations, which will be developed in Paper II of this series.
Show PACS
02.20.Sv Lie algebras of Lie groups
02.30.Hq Ordinary differential equations
11.10.Lm Nonlinear or nonlocal theories and models
11.30.Na Nonlinear and dynamical symmetries (spectrum-generating symmetries)

Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two‐component spinors

D. Han, Y. S. Kim, and D. Son

J. Math. Phys. 27, 2228 (1986); http://dx.doi.org/10.1063/1.526994 (8 pages) | Cited 30 times

Full Text: | Download PDF

Show Abstract
A set of rotations and Lorentz boosts is presented for studying the three‐parameter little groups of the Poincaré group. This set constitutes a Lorentz generalization of the Euler angles for the description of classical rigid bodies. The concept of Lorentz‐generalized Euler rotations is then extended to the parametrization of the E(2)‐like little group and the O(2,1)‐like little group for massless and imaginary‐mass particles, respectively. It is shown that the E(2)‐like little group for massless particles is a limiting case of the O(3)‐like or O(2,1)‐like little group. A detailed analysis is carried out for the two‐component SL(2,c) spinors. It is shown that the gauge degrees of freedom associated with the translationlike transformation of the E(2)‐like little group can be traced to the SL(2,c) spins that fail to align themselves to their respective momenta in the limit of large momentum and/or vanishing mass.
Show PACS
02.20.Rt Discrete subgroups of Lie groups
02.20.Bb General structures of groups
03.30.+p Special relativity
11.30.Cp Lorentz and Poincaré invariance

Generating relations for reducing matrices. II. Corepresentations

M. I. Aroyo, J. N. Kotzev, M. N. Angelova‐Tjurkedjieva, R. Dirl, and P. Kasperkovitz

J. Math. Phys. 27, 2236 (1986); http://dx.doi.org/10.1063/1.526995 (11 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
The auxiliary group approach developed in Paper 1 [R. Dirl, P. Kasperkovitz, M. I. Aroyo, J. N. Kotzev, and M. Angelova‐Tjurkedjieva, J. Math. Phys. 27, 37 (1986)] is generalized for the case of corepresentations of antiunitary groups. It allows us to reduce the multiplicity problem and to derive consistent generating relations for the elements of the reducing matrices for coreps. Two examples are worked out to illustrate the general scheme.
Show PACS
02.20.Qs General properties, structure, and representation of Lie groups

Analysis on generalized superspaces

Yuji Kobayashi and Shigeaki Nagamachi

J. Math. Phys. 27, 2247 (1986); http://dx.doi.org/10.1063/1.526996 (10 pages) | Cited 5 times

Full Text: | Download PDF

Show Abstract
The analysis over σ‐commutative algebras (generalized supercommutative algebras), that is, differentiation and integration for functions defined on superspace over a σ‐commutative algebra, is studied.
Show PACS
02.20.Sv Lie algebras of Lie groups
02.30.Uu Integral transforms
02.30.Vv Operational calculus
02.40.Vh Global analysis and analysis on manifolds

Linearization and Painlevé property of Liouville and Cheng equations

K. M. Tamizhmani and M. Lakshmanan

J. Math. Phys. 27, 2257 (1986); http://dx.doi.org/10.1063/1.526997 (2 pages) | Cited 6 times

Full Text: | Download PDF

Show Abstract
It is demonstrated that the Liouville equation and the Cheng equation (describing a chemical reaction) are free from movable critical manifolds and possess the Painlevé property. The associated linearizing transformations and general solutions follow naturally from the Painlevé analysis.
Show PACS
02.30.Jr Partial differential equations
41.20.Jb Electromagnetic wave propagation; radiowave propagation
45.05.+x General theory of classical mechanics of discrete systems

The anomaly structure of theories with external gravity

L. Bonora, P. Pasti, and M. Tonin

J. Math. Phys. 27, 2259 (1986); http://dx.doi.org/10.1063/1.526998 (12 pages) | Cited 16 times

Full Text: | Download PDF

Show Abstract
The cohomology problem of the overall local symmetry group of theories with external gravity, including diffeomorphisms, local Lorentz, and gauge transformations, is studied, in order to determine all possible anomalies. To this end the nontrivial cohomology classes of the coupled system of two coboundary operators are classified in the abstract. Using this result and a technical assumption the nontrivial cohomology classes of the coboundary operator associated with diffeomorphisms are determined. These possible anomalies split in any dimension into two distinct families. Both are calculated (the second only in four dimensions). Using known results about gauge and local Lorentz anomalies, the possible anomalies of the overall local symmetry group are determined.
Show PACS
02.40.Ma Global differential geometry
02.40.Hw Classical differential geometry
02.20.Rt Discrete subgroups of Lie groups
11.30.-j Symmetry and conservation laws

A path‐integral–Riemann‐space approach to the electromagnetic wedge diffraction problem

Richard W. Ziolkowski

J. Math. Phys. 27, 2271 (1986); http://dx.doi.org/10.1063/1.526999 (11 pages) | Cited 6 times

Full Text: | Download PDF

Show Abstract
A path integral constructed over a particular Riemann space is developed and applied to two‐dimensional wedge problems. This path‐integral–Riemann‐space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. A high‐frequency asymptotic evaluation of the PIRS electromagnetic wedge solution returns the standard geometrical theory of diffraction (GTD) results. Ramifications of this approach and its relationships with known path‐integral methods are examined.
Show PACS
41.20.Jb Electromagnetic wave propagation; radiowave propagation
02.60.Lj Ordinary and partial differential equations; boundary value problems
03.65.Fd Algebraic methods

Group‐related coherent states

Anton Amann

J. Math. Phys. 27, 2282 (1986); http://dx.doi.org/10.1063/1.527000 (8 pages) | Cited 4 times

Full Text: | Download PDF

Show Abstract
Coherent states defined with respect to an irreducible ray representation u: g→ug, g∊G, of an arbitrary locally compact separable group G are examined. It is shown that the following conditions (a)–(d) are equivalent: (a) u admits coherent states, (b) u is square integrable, (c) the W∗‐system implemented by u is integrable, and (d) u is a subrepresentation of the left regular c‐representation, where c is the respective multiplier of u. Furthermore, the group theoretical background of what is called the ‘‘P‐representation of observables’’ associated with coherent states is investigated: It is shown that the P‐representation (which corresponds to a covariant semispectral measure) fulfills a certain maximality requirement. The P‐representation can be used to represent the quantum system in question on the Hilbert space L2(G,dg) of square‐integrable functions (with respect to Haar measure dg) on the kinematical group G.
Show PACS
03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Db Functional analytical methods
03.65.Fd Algebraic methods

Evolution loops

Bogdan Mielnik

J. Math. Phys. 27, 2290 (1986); http://dx.doi.org/10.1063/1.527001 (17 pages) | Cited 21 times

Full Text: | Download PDF

Show Abstract
The problem of manipulating Schrödinger’s particle by time‐dependent external fields is discussed. New solutions of the evolution problem, called evolution loops, are found. They correspond to the ‘‘particle memory’’ in the sense of Brewer and Hahn [Sci. Am. 251(12), 50 (1984)]. A technique of generating the unitary operations by perturbing the evolution loops is outlined.
Show PACS
03.65.Ta Foundations of quantum mechanics; measurement theory
45.05.+x General theory of classical mechanics of discrete systems
05.30.-d Quantum statistical mechanics

Variational processes and stochastic versions of mechanics

J. C. Zambrini

J. Math. Phys. 27, 2307 (1986); http://dx.doi.org/10.1063/1.527002 (24 pages) | Cited 45 times

Full Text: | Download PDF

Show Abstract
The dynamical structure of any reasonable stochastic version of classical mechanics is investigated, including the version created by Nelson [E. Nelson, Quantum Fluctuations (Princeton U.P., Princeton, NJ, 1985); Phys. Rev. 150, 1079 (1966)] for the description of quantum phenomena. Two different theories result from this common structure. One of them is the imaginary time version of Nelson’s theory, whose existence was unknown, and yields a radically new probabilistic interpretation of the heat equation. The existence and uniqueness of all the involved stochastic processes is shown under conditions suggested by the variational approach of Yasue [K. Yasue, J. Math. Phys. 22, 1010 (1981)].
Show PACS
02.50.Ey Stochastic processes
02.50.Fz Stochastic analysis
03.65.Ta Foundations of quantum mechanics; measurement theory
45.05.+x General theory of classical mechanics of discrete systems

Large‐N solution of the Klein–Gordon equation

Ashok Chatterjee

J. Math. Phys. 27, 2331 (1986); http://dx.doi.org/10.1063/1.527003 (5 pages) | Cited 22 times

Full Text: | Download PDF

Show Abstract
An iterative 1/N expansion scheme is developed to solve the Klein–Gordon equation to obtain the energy spectrum of a scalar particle in a spherically symmetric potential. For the Coulomb potential, this approach is shown to yield the exact results.
Show PACS
03.65.Ge Solutions of wave equations: bound states
03.65.Fd Algebraic methods

Conformal transformations and viscous fluids in general relativity

J. Carot and Ll. Mas

J. Math. Phys. 27, 2336 (1986); http://dx.doi.org/10.1063/1.527004 (4 pages) | Cited 9 times

Full Text: | Download PDF

Show Abstract
It is shown that viscous fluid solutions can be obtained by performing conformal transformations of vacuum solutions of Einstein’s field equations. The solutions obtained by such a procedure can be matched, under certain conditions, to their respective original vacuum metrics.
Show PACS
04.20.Jb Exact solutions
04.20.Fy Canonical formalism, Lagrangians, and variational principles

A class of perfect fluid metrics with flat three‐dimensional hypersurfaces

Thomas Wolf

J. Math. Phys. 27, 2340 (1986); http://dx.doi.org/10.1063/1.527005 (14 pages) | Cited 1 time

Full Text: | Download PDF

Show Abstract
The class of perfect fluid and vacuum space‐times with a family of flat three‐slices and a tensor of exterior curvature covariantly constant within these slices is examined and the corresponding solutions are found. It is shown that this class contains the class of metrics with three commuting Killing vectors. Therefore, e.g., all known stationary metrics with cylindrical or plane symmetry are generalized. An instruction is given for constructing perfect fluid metrics with this symmetry and a connection to a vacuum across surfaces p=0. Thereby the equation of state of the interior rotating perfect fluid can be arbitrarily chosen and the positivity of density and pressure can be forced. A geometric criterion of the interior metric with rotating matter is found that decides whether the exterior solution is stationary or static. Besides solutions with three symmetries, inhomogeneous metrics also are found. Among them is a solution with one symmetry and rotating, expanding, shearing, and accelerating perfect fluid. All resulting vacuum solutions are already known.
Show PACS
04.20.Jb Exact solutions
95.30.Sf Relativity and gravitation
02.40.Ky Riemannian geometries

About vacuum solutions of Einstein’s field equations with flat three‐dimensional hypersurfaces

Thomas Wolf

J. Math. Phys. 27, 2354 (1986); http://dx.doi.org/10.1063/1.527006 (6 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
The class of vacuum space‐times with a family of flat three‐slices and a traceless tensor of exterior curvature Kab is examined. Metrics without symmetry and solutions describing gravitational radiation are obtained. It turns out that there is a correlation between rank (Kab) and the Petrov type. Although the resulting solutions are already known, the richness of the class of space‐times with flat slices becomes obvious. An example is given of a metric with one‐parameter manifold of families of flat slices.
Show PACS
04.20.Jb Exact solutions
02.40.Ky Riemannian geometries

An example of affine collineation in the Robertson–Walker metric

M. L. Bedran and B. Lesche

J. Math. Phys. 27, 2360 (1986); http://dx.doi.org/10.1063/1.527007 (2 pages) | Cited 8 times

Full Text: | Download PDF

Show Abstract
An affine collineation for the Robertson–Walker metric is found. It implies a condition on the metric that is compatible with Einstein’s equations for a perfect fluid satisfying the Hawking–Ellis energy conditions. It is shown how the geodesics of the metric are obtained from the constant of motion associated to the affine collineation.
Show PACS
04.20.-q Classical general relativity
02.40.Ky Riemannian geometries

Gravitational solutions, including radiation, for a perturbed light beam

Raymond W. Nackoney

J. Math. Phys. 27, 2362 (1986); http://dx.doi.org/10.1063/1.527393 (11 pages) | Cited 1 time

Full Text: | Download PDF

Show Abstract
Linearized field equations and solutions are derived for a perturbed sheet beam of light. The work is based on an exact solution of a collimated beam in the geometrical limit. The linearized field changes of the initially curved background metric can be put, with the help of the harmonic conditions, into a normal coordinate form. These six normal coordinates satisfy six linearized, inhomogeneous, field equations in three variables. Stationary solutions include divergent beams. Gravitational waves propagating opposite to the beam’s flux are found to be confined to a region about the propagation axis of the beam, much as is experienced in wave guides. Radiative cases can be produced by large angle scattering of light and are discussed in terms of their effect on an ideal optical antenna. The effect is one that grows linearly with time. The growth time is prohibitively long for the most energetic systems that can be realistically considered in the foreseeable future.
Show PACS
04.30.-w Gravitational waves
04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime
04.20.Jb Exact solutions
95.30.Sf Relativity and gravitation

Three remarks on Powers’ theorem about irreducible fields fulfilling CAR

Klaus Baumann

J. Math. Phys. 27, 2373 (1986); http://dx.doi.org/10.1063/1.527008 (6 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
First it is shown that within a relativistic Fermi field theory, a bound ∥Ψk( f,t)∥ ≤C∥ f ∥2 already implies canonical anticommutation relations (CAR). Then under Powers’ assumptions a linear, first‐order differential equation for the fields ψk(x,t) is derived. This shows that in the set of generalized free fields fulfilling CAR only the free fields are irreducible at time zero. Finally Fermi fields in two space‐time dimensions are considered. It is shown that only four‐fermion interaction might be compatible with CAR and a bound on the coupling strength is derived.
Show PACS
11.10.Cd Axiomatic approach
11.10.Kk Field theories in dimensions other than four
02.40.Ky Riemannian geometries

Four‐dimensional boson field theory. II. Existence

George A. Baker

J. Math. Phys. 27, 2379 (1986); http://dx.doi.org/10.1063/1.527009 (15 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high‐temperature expansions of the corresponding continuous‐spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free.
Show PACS
11.10.Jj Asymptotic problems and properties
11.10.Kk Field theories in dimensions other than four
11.15.Bt General properties of perturbation theory
11.10.Lm Nonlinear or nonlocal theories and models

Formal power series solutions of supersymmetric (N=3) Yang–Mills equations

J. Harnad and M. Jacques

J. Math. Phys. 27, 2394 (1986); http://dx.doi.org/10.1063/1.527010 (8 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
Formal power series solutions of the linear system with one spectral parameter associated to the constraint equations for Yang–Mills superconnections on N‐extended super‐Minkowski space are considered. For N=3 the integrability equations reduce to the supersymmetric field equations. The method of approach is identical to that used by Takasaki for the self‐dual equations, based upon formal power series in a spectral parameter and in spatial variables. The problem is reduced to a linear system of equations for a superfield with values in an ∞‐dimensional Grassmann manifold. The formal solution is expressed in terms of data on a (3‖2N)‐dimensional superhypersurface. However, a difficulty arises with respect to the Cauchy problem, which becomes formally solvable only for an extended system, breaking the relativistic invariance through introduction of additional superfields.
Show PACS
11.10.Jj Asymptotic problems and properties
11.30.Pb Supersymmetry
11.15.Ex Spontaneous breaking of gauge symmetries

On the formulation of the positive‐energy theorem in Kaluza–Klein theories

Osvaldo M. Moreschi and George A. J. Sparling

J. Math. Phys. 27, 2402 (1986); http://dx.doi.org/10.1063/1.527011 (7 pages) | Cited 7 times

Full Text: | Download PDF

Show Abstract
The positive‐energy theorem is formulated in the context of Kaluza–Klein theories. Different cases are considered, including the situation in which no symmetry is assumed. This work offers a new technique for stability considerations in Kaluza–Klein theories.
Show PACS
11.10.Kk Field theories in dimensions other than four
04.50.-h Higher-dimensional gravity and other theories of gravity
04.60.-m Quantum gravity

Conformal quantum Yang–Mills

A. D. Haidari

J. Math. Phys. 27, 2409 (1986); http://dx.doi.org/10.1063/1.526979 (6 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
Conformally covariant quantization of non‐Abelian gauge theory is presented, and the invariant propagators needed for perturbative calculations are found. The vector potential acquires a richer gauge structure displayed in the larger Gupta–Bleuler triplet whose center is occupied by conformal QED. Path integral formulation and BRS invariance are shown on a formal level in one covariant gauge.
Show PACS
11.30.Ly Other internal and higher symmetries
02.20.Qs General properties, structure, and representation of Lie groups
12.20.Ds Specific calculations

Gauge theory of a group of diffeomorphisms. I. General principles

Eric A. Lord and P. Goswami

J. Math. Phys. 27, 2415 (1986); http://dx.doi.org/10.1063/1.526980 (8 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
Any (N+M)‐parameter Lie group G with an N‐parameter subgroup H can be realized as a global group of diffeomorphisms on an M‐dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space‐time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities.
Show PACS
11.15.-q Gauge field theories
11.10.Ef Lagrangian and Hamiltonian approach
11.30.-j Symmetry and conservation laws

Scalar formalism for non‐Abelian gauge theory

Levere C. Hostler

J. Math. Phys. 27, 2423 (1986); http://dx.doi.org/10.1063/1.526981 (6 pages) | Cited 4 times

Full Text: | Download PDF

Show Abstract
The gauge field theory of an N‐dimensional multiplet of spin‐ 1/2 particles is investigated using the Klein–Gordon‐type wave equation {Π ⋅ (1+iσ) ⋅ Π+m2}Φ=0, Πμ≡∂/∂ixμ−eAμ, investigated before by a number of authors, to describe the fermions. Here Φ is a 2×1 Pauli spinor, and σ repesents a Lorentz spin tensor whose components σμν are ordinary 2×2 Pauli spin matrices. Feynman rules for the scalar formalism for non‐Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum τ‐functions, τ(2,1, ⋅⋅⋅ 3 ⋅⋅⋅)≡〈0−‖T(Ψin(2) Ψin(1) ⋅⋅⋅ Aμ(3)in ⋅⋅⋅ S)‖0−〉, where Ψin is a Heisenberg operator belonging to a 4N×1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics.
Show PACS
11.15.Bt General properties of perturbation theory
03.65.Pm Relativistic wave equations
12.20.Ds Specific calculations

Spectra of supersymmetric O(N) sigma models in 0+1 dimension

B. Sathiapalan

J. Math. Phys. 27, 2429 (1986); http://dx.doi.org/10.1063/1.526982 (5 pages) | Cited 1 time

Full Text: | Download PDF

Show Abstract
The spectra of the supersymmetric O(N) nonlinear sigma models in 0+1 space‐time dimension are computed exactly for any N, using group theoretical methods. The allowed representations are O(N) analogs of the Wigner d functions.
Show PACS
11.30.Pb Supersymmetry
11.10.Kk Field theories in dimensions other than four
11.10.Ef Lagrangian and Hamiltonian approach
02.20.Rt Discrete subgroups of Lie groups

The Schwinger–DeWitt proper‐time method for odd‐dimensional gauge theory

Taejin Lee

J. Math. Phys. 27, 2434 (1986); http://dx.doi.org/10.1063/1.527392 (3 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
The Schwinger–DeWitt proper‐time method (WKB expansion) is applied to calculate the anomaly in odd‐dimensional gauge theories. The parity violating part of effective action for gauge theory in odd dimensions with massless fermion is calculated explicitly and efficiently by this method. It is shown to be precisely the local Chern–Simons term.
Show PACS
11.30.Qc Spontaneous and radiative symmetry breaking
11.15.Ex Spontaneous breaking of gauge symmetries
11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries
11.30.Rd Chiral symmetries
Page 1 of 2 Pages Next Page | Jump to Page
Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Erratum: Imparting to a Bianchi type II space‐time [J. Math. Phys. 27, 417 (1986)]
  2. Statistical filter theory and the O’Doherty–Anstey effect: Dependence on offset
  3. Erratum: On a labeling for point group harmonics. I and II [J. Math. Phys. 26, 2413, 2441 (1985)]
  4. Coherent states of the real symplectic group in a complex analytic parametrization. II. Annihilation‐operator coherent states
  5. Mathematical aspects of quantum fluids. III. Interior Clebsch representations and transformations of symplectic two‐cocycles for 4He
Go to AIP Home
Copyright © American Institute of Physics
close