Related papers: General field theory and weak Euler-Lagrange equat…
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
We analyze the general radiation emission mechanism from a charged particle moving in a curved inhomogeneous magnetic field. The consideration of the gradient makes the curved vacuum magnetic field compatible with the Maxwell equations and…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson…
We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field…
It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
For many purposes, classical plasma dynamics models can work surprisingly well even for strong electromagnetic fields, approaching the Schwinger critical fields, and high frequencies, approaching the Compton frequency. However, the…
English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…
We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
The general-relativistic Ohm's law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
We explore global Poisson-Lie (PL) symmetries using a Lagrangian, or "covariant phase space" approach, that manifestly preserves spacetime covariance. PL symmetries are the classical analog of quantum-group symmetries. In the Noetherian…
Based on investigations of the fundamental properties of the generalized Einstein Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein field equations and the Lorentz and Levi-Civita…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…