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