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Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
We introduce a general approximation scheme in order to calculate gauge invariant observables in the canonical formulation of general relativity. Using this scheme we will show how the observables and the dynamics of field theories on a…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
A proposal for the issue of time and observables in any parameterized theory such as general relativity is addressed. Introduction of a gauge potential 3-form A in the theory of relativity enables us to define a gauge-invariant quantity…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
We investigate generally covariant theories which admit a Fierz-Pauli mass term for metric perturbations around an arbitrary curved background. For this we restore the general covariance of the Fierz-Pauli mass term by introducing four…
The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante…
We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical…
By taking into account both quantum mechanical and general relativistic effects, I derive an equation that describes limitations on the measurability of space-time distances as defined by a material reference system.
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
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 high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…