Related papers: Relativistic Elastomechanics is a Gauge--Type Theo…
In this work we discuss different interpretations of mass in the relativistic dynamics. A new way to introduce mass is proposed. Our way is based on the relativistic equation of motion expressed in the form of the Newton$'$s second law. In…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
We investigate the dynamics of three-dimensional lattice gauge theories by means of an external Abelian magnetic field. For the SU(2) lattice gauge theory we find evidence of the unstable modes.
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In this third paper we elevate the Newtonian theory of the…
First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a…
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed…
The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of…
We study the action and the dynamics of a relativistic particle, uncharged or charged, in multiscale spacetimes. Invariance under reparametrizations and Poincar\'e symmetries uniquely determine the action and the line element to be the…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…
We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the…
A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in…
We present important elements of a gauge and diffeomorphism invariant formulation of the moduli space approximation to soliton dynamics. We argue that explicit velocity-dependent modifications are determined entirely from gauge and…
This short note is devoted to the Hamiltonian analysis of three dimensional gravity action that was proposed recently in [arXiv:1309.7231]. We modify given action in order to be invariant under non-relativistic diffeomorphism. Then we…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
The construction of Dirac observables, that is gauge invariant objects, in General Relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely…
A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial…