相关论文: Nonrelativistic and Relativistic Continuum Mechani…
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality…
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the…
After a short introduction to the characteristic geometry underlying weakly hyperbolic systems of partial differential equations we review the notion of symmetric hyperbolicity of first-order systems and that of regular hyperbolicity of…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
The numerical solutions of the nonrelativistic and relativistic Boltzmann equations have been studied at various initial conditions. Particularly, the known analytical solution of the nonrelativistic Boltzmann equation at spherically…
We construct time independent configurations describing a small elastic body moving in a circular orbit in the Schwarzschild spacetime. These configurations are relativistic versions of Newtonian solutions constructed previously by us. In…
Relative Locality is a recent approach to the quantum-gravity problem which allows to tame nonlocality effects which may rise in some models which try to describe Planck-scale physics. I here explore the effect of Relative Locality on basic…
Closed nonrelativistic (nonretarded) theory of conservative and dissipative electromagnetic forces and heat exchange between moving particles (nanoprobes) and a surface (flat and cylindrical) is reviewed. The formalism is based on methods…
A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented,…
In the light of some recent results, it is argued that usual concepts of causality and locality are approximations valid at scales greater than the Compton wavelength and corresponding time scales. It follows that the "spooky" non-locality…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…
The validity of non-perturbative methods is questioned. The concept of relative space is introduced.
We show that the relativistic gravity theory can offer a framework to formulate the non-relativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2+1 dimensions which is particularly…
I briefly discuss the construction of a theory of particles with curved momentum space and its consequence, the principle of relative locality.
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…