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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…
In Newtonian physics, the excitation spectrum of a fluid is the same in all reference frames, up to a trivial shift. In special relativity, this is no longer the case. Relativity of simultaneity causes different inertial observers to…
The direction of polarization produced by a moving source rotates with the respect to the rest frame. We show that this effect, induced by pulsar rotation, leads to an important correction to polarization swings within the framework of…
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…
The study of relativistic Coulomb systems in velocity space is prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space, although less familiar than the analytic solutions in ordinary space, provides a much…
We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in…
Following an early observation of Ignatowsky, we present a derivation of the transformation rules between inertial systems making no other assumptions than the existence of the latter, and show that generically these rules are characterized…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
The analysis of the dynamics of radial movement in different reference frames used in cosmology is made. Use of different frames leads to the difference in inertial forces resulting in different observable effects. The important effect is…
A Reference is corrected. (We derive the Fermi coordinate system of an observer in arbitrary motion in an arbitrary weak gravitational field valid to all orders in the geodesic distance from the worldline of the observer. In flat space-time…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…