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We give a general definition of \emph{relativistic force} in the context of Lagrangian mechanics. Once this is done we prove that the only relativistic forces which are linear on the velocities are th...
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems wh...
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the grav...
Abstract: We present a formulation of relativistic classical and quantum mechanics in the Hilbert space with a linkage through the Ehrenfest quantization. We start with the covariant form of the Loren...
Abstract: The relativistic Fokker-Planck equation, in which the speed of light $c$ appears as a parameter, is considered. It is shown that in the limit $c\to\infty$ its solutions converge in $L^1$ to ...
Abstract: We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in...
Abstract: Spin current of a Dirac particle is shown to be given by the geometric phase and in terms of the later, a closed form expression is obtained for the dissipationlessness of the spin current.
Abstract: We inquire into classical and quantum laws of motion for the point charge sources in the nonlinear Maxwell-Born-Infeld field equations of classical electromagnetism in flat and curved Einste...
Abstract: We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponen...
Abstract: We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The var...
Abstract: In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We inte...
Abstract: The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of stat...
Abstract: We develop a suitable generalization of Almgrens theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by ...
Abstract: We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulo...
Using the AMPT model for relativistic heavy ion collisions, we have studied the di-hadron azimuthal angular correlations triggered by emitted jets in Au+Au collisions at center of mass energy psNN = 2...

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