Related papers: Relativistic Wave Equations in the Helicity Basis
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar-tensor representation. It turns out that the stellar structure equations can be written with respect to the…
We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group. The particle case is meant to clarify some points…
Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields perpendicular to the direction of propagation? This is an…
We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion,…
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
A generalized top-spin analysis proposed some time ago in the context of Standard Model and subsequently studied in varying contexts is now applied primarily to the case of $e^+e^-\rightarrow t\bar{t}$ with transversely polarized beams.…
Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to…
Within the framework of relativistic theory of gravitation the exact spherically-symmetric wave solution is received. It is shown that this solution possesses the positive-definite energy and momentum deriving with the Fock energy-momentum…