81 research outputs found
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
Relativistic Coulomb problem for particles with arbitrary half-integer spin
Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we
solve the Kepler problem for a charged particle with arbitrary half-integer
spin interacting with the Coulomb potential.Comment: Misprints are correcte
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
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
Relation between confinement and higher symmetry restrictions for color particle motion
Quantum operators of coordinates and momentum components of a particle in the
Minkowski spacetime can belong to the generalized Snyder-Yang algebra and
produce a quantum phase space with three new constants in the general case.
With account for the O(2,6) invariance in the quantum phase space of a color
particle the equation of motion is obtained, which contains a oscillator rising
potential. The presence of the oscillator potential can simulate a confinement
of a color particle. A parameter of the oscillator potential is estimated and a
relationship between current and constituent quark masses is obtained.Comment: 3 pages, style and typos corrected, more general case considered,
main results unchange
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
Hierarchy of Conservation Laws of Diffusion--Convection Equations
We introduce notions of equivalence of conservation laws with respect to Lie
symmetry groups for fixed systems of differential equations and with respect to
equivalence groups or sets of admissible transformations for classes of such
systems. We also revise the notion of linear dependence of conservation laws
and define the notion of local dependence of potentials. To construct
conservation laws, we develop and apply the most direct method which is
effective to use in the case of two independent variables. Admitting
possibility of dependence of conserved vectors on a number of potentials, we
generalize the iteration procedure proposed by Bluman and Doran-Wu for finding
nonlocal (potential) conservation laws. As an example, we completely classify
potential conservation laws (including arbitrary order local ones) of
diffusion--convection equations with respect to the equivalence group and
construct an exhaustive list of locally inequivalent potential systems
corresponding to these equations.Comment: 24 page
Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields
A general method of the Foldy-Wouthyusen (FW) transformation for relativistic
particles of arbitrary spin in strong external fields has been developed. The
use of the found transformation operator is not restricted by any definite
commutation relations between even and odd operators. The final FW Hamiltonian
can be expanded into a power series in the Planck constant which characterizes
the order of magnitude of quantum corrections. Exact expressions for low-order
terms in the Planck constant can be derived. Finding these expressions allows
to perform a simple transition to the semiclassical approximation which defines
a classical limit of the relativistic quantum mechanics. As an example,
interactions of spin-1/2 and scalar particles with a strong electromagnetic
field have been considered. Quantum and semiclassical equations of motion of
particles and their spins have been deduced. Full agreement between quantum and
classical theories has been established.Comment: 10 page
- …