Related papers: Non-universal relativistic kinematics
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
In this paper, we define a new velocity having a dimension of $(Length)^{\alpha}/(Time)$ and a new acceleration having a dimension of $(Length)^{\alpha}/(Time)^2$, based on the fractional addition rule. We then discuss the fractional…
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…
The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain…
A particular problem about special kind of two light pulses propagation has been considered in cases of inertial motion, constant homogeneous gravitation field and progressive non-inertial motion with constant acceleration. A contradiction…
We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
Astronomical observations have a unique ability to determine the laws of physics at distant times in the universe. They, therefore, have particular relevance in answering the basic question as to whether the laws of physics are invariant…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space…
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 consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…