Related papers: General Solutions of Relativistic Wave Equations I…
Based on the representation theory of the $q$-deformed Lorentz and Poincar\'e symmeties $q$-deformed relativistic wave equation are constructed. The most important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations are…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein Gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin…
Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like space-time models allow the existence of privileged coordinate systems where the…
The theory of relativistic strings is considered in frames of Hamiltonian formalism and Dirac's quantization procedure. A special gauge fixing condition is formulated, related with the world sheet of the string in Lorentz-invariant way. As…
Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity…
New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of…
The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry…
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincar\'e group, it is possible to construct representations of the little group for massive particles starting from harmonic…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
We give a brief overview of the BRST approach to the gauge invariant Lagrangian formulation for free massive higher-spin bosonic fields focusing on two specific aspects. First, the theory is considered in four dimensional flat space in…
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…
In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the…
We consider a massive particle of arbitrary spin and the basis vectors that carry the unitary, irreducible representations of the Poincar\'e group. From the complex coefficients in normalizable superpositions of these basis vectors, we…
A class of Siklos waves, representing exact vacuum solutions of general relativity with a cosmological constant, is extended to a new class of Siklos waves with torsion, defined in the framework of the Poincar\'e gauge theory. Three…
A massive relativistic spinning point particle in any number of dimensions has in a previous article been shown to be described by first class constraints, which define a gauge theory. In the present paper we find the corresponding finite…
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincar\'e dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to…