191 research outputs found
On a possible approach to the variable-mass problem
The mass operator M is introduced as an independent dynamical variable which
is taken as the translation generator P_4 of the inhomogenous De Sitter group.
The classification of representations of the algebra P(1,4) of this group is
performed and the corresponding P(1,4) invariant equations for variable-mass
particles are written out. In this way we have succeeded, in particular, in
uniting the ``external'' and ``internal'' (SU_2) symmetries in a non-trivial
fashion.Comment: 4 page
On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics
Recent experimental results on slow light heighten interest in nonlinear
Maxwell theories. We obtain Galilei covariant equations for electromagnetism by
allowing special nonlinearities in the constitutive equations only, keeping
Maxwell's equations unchanged. Combining these with linear or nonlinear
Schroedinger equations, e.g. as proposed by Doebner and Goldin, yields a
Galilean quantum electrodynamics.Comment: 12 pages, added e-mail addresses of the authors, and corrected a
misprint in formula (2.10
Lorentz Multiplet Structure of Baryon Spectra and Relativistic Description
The pole positions of the various baryon resonances are known to reveal
well-pronounced clustering, so-called Hoehler clusters. For nonstrange baryons
the Hoehler clusters are shown to be identical to Lorentz multiplets of the
type (j,j)*[(1/2,0)+(0,1/2)] with j being a half-integer. For the Lambda
hyperons below 1800 MeV these clusters are shown to be of the type [(1,0)+
(0,1)]*[(1/2,0)+(0,1/2)] while above 1800 MeV they are parity duplicated
(J,0)+(0,J) (Weinberg-Ahluwalia) states. Therefore, for Lambda hyperons the
restoration of chiral symmetry takes place above 1800 MeV. Finally, it is
demonstrated that the description of spin-3/2 particles in terms of a 2nd rank
antisymmetric Lorentz tensor with Dirac spinor components does not contain any
off-shell parameters and avoids the main difficulties of the Rarita-Schwinger
description based upon a 4-vector with Dirac spinor components.Comment: 12 pages, LaTex, submitted to Mod. Phys. Lett.
A tree of linearisable second-order evolution equations by generalised hodograph transformations
We present a list of (1+1)-dimensional second-order evolution equations all
connected via a proposed generalised hodograph transformation, resulting in a
tree of equations transformable to the linear second-order autonomous evolution
equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia
"Minus c" Symmetry in Classical and Quantum Theories
It is shown that the transformations of the charge conjugation in classical
electrodynamics and in quantum theory can be interpreted as the consequences of
the symmetry of Maxwell and Dirac equations with respect to the inversion of
the speed of light: c to -c; t to t; (x,y,z) to (x,y,z), where c is the speed
of light; t is the time; x, y, z are the spatial variables.
The elements of physical interpretation are given.Comment: 12 pages, LaTeX, Poster at the Fifth International Conference on
Squeezed States and Uncertainty Relations, May 27-31, 1997, Balatonfured,
Hungar
Group analysis of a class of nonlinear Kolmogorov equations
A class of (1+2)-dimensional diffusion-convection equations (nonlinear
Kolmogorov equations) with time-dependent coefficients is studied with Lie
symmetry point of view. The complete group classification is achieved using a
gauging of arbitrary elements (i.e. via reducing the number of variable
coefficients) with the application of equivalence transformations. Two possible
gaugings are discussed in detail in order to show how equivalence groups serve
in making the optimal choice.Comment: 12 pages, 4 table
Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time
A classification of all possible realizations of the Galilei,
Galilei-similitude and Schroedinger Lie algebras in three-dimensional
space-time in terms of vector fields under the action of the group of local
diffeomorphisms of the space \R^3\times\C is presented. Using this result a
variety of general second order evolution equations invariant under the
corresponding groups are constructed and their physical significance are
discussed
New exactly solvable relativistic models with anomalous interaction
A special class of Dirac-Pauli equations with time-like vector potentials of
external field is investigated. A new exactly solvable relativistic model
describing anomalous interaction of a neutral Dirac fermion with a
cylindrically symmetric external e.m. field is presented. The related external
field is a superposition of the electric field generated by a charged infinite
filament and the magnetic field generated by a straight line current. In
non-relativistic approximation the considered model is reduced to the
integrable Pron'ko-Stroganov model.Comment: 20 pages, discussion of the possibility to test the model
experimentally id added as an Appendix, typos are correcte
Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions
All indecomposable finite-dimensional representations of the homogeneous
Galilei group which when restricted to the rotation subgroup are decomposed to
spin 0, 1/2 and 1 representations are constructed and classified. These
representations are also obtained via contractions of the corresponding
representations of the Lorentz group. Finally the obtained representations are
used to derive a general Pauli anomalous interaction term and Darwin and
spin-orbit couplings of a Galilean particle interacting with an external
electric field.Comment: 23 pages, 2 table
Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
We consider the Klein-Gordon equation in generalized higher-dimensional
Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional
parameters characterizing the metric. We establish commutativity of the
second-order operators constructed from the Killing tensors found in
arXiv:hep-th/0612029 and show that these operators, along with the first-order
operators originating from the Killing vectors, form a complete set of
commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon
equation. Moreover, we demonstrate that the separated solutions of the
Klein-Gordon equation obtained in arXiv:hep-th/0611245 are joint eigenfunctions
for all of these operators. We also present explicit form of the zero mode for
the Klein-Gordon equation with zero mass.
In the semiclassical approximation we find that the separated solutions of
the Hamilton-Jacobi equation for geodesic motion are also solutions for a set
of Hamilton-Jacobi-type equations which correspond to the quadratic conserved
quantities arising from the above Killing tensors.Comment: 6 pages, no figures; typos in eq.(6) fixed; one reference adde
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