Related papers: Discrete phase space - I: Variational formalism fo…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first order Lagrangian by boundary terms only. A new method of deriving…
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
Classical description of relativistic pointlike particle with intrinsic degrees of freedom such as isospin or colour is proposed. It is based on the Lagrangian of general form defined on the tangent bundle over a principal fibre bundle. It…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
We generalize the fractional Caputo derivative to the fractional derivative ${^CD^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional derivative…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
We obtain several Euler-Lagrange equations for variational functionals defined on a set of H\"older curves. The cases when the Lagrangian contains multiple scale derivatives, depends on a parameter, or contains higher-order scale…
This paper is devoted to the initial value problems for semilinear wave equations of derivative type with spatial weights in one space dimension. The lifespan estimates of classical solutions are quite different from those for nonlinearity…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end…
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one…
A relativistic equation for a neutral complex field as a probability amplitude is proposed. The continuity equation for the probability density is obtained. It is shown that there are two types of excitations of this field, which describe…
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…