相关论文: A Local Gauge-Covariant Formulation of Classical D…

Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…

We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…

Irreversibility implies a preferred flow of time, yet special relativity denies the existence of a preferred clock. This tension has long obstructed the formulation of a relativistic master equation: standard Markovian approximations either…

A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…

An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…

Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the…

Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population…

Gauge fields frequently used as an independent construction additional to so-called wave fields of matter. This artificial separation is of course useful in some applications (like Berry's interactions between the "heavy" and "light"…

We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…

Conformal gravity on noncommutative spacetime is considered in this paper. The presupposed gravity action consists of the Brans-Dicke gravity action with a special prefactor of the term, where the Ricci scalar couples to the scalar field,…

The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization…

It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…

Non-perturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are…

The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of…

We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…

We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…

Discrete Ginzburg-Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two…

Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…

In the first part of the thesis we focus on local symmetries. We review a self-consistent framework that we employed in order to discuss the dynamics of the theories of interest. Its merit lies in that we can make the symmetry group act…