相关论文: Exterior Differential Forms in Field Theory

In this paper, we generalize De Donder approach to construct boundary forms that depend on the adapted coordinate system used. In continuum mechanics, use of boundary forms leads to splitting of the total force acting on the body into body…

Identical relations occur in various branches of mathematics and mathematical physics. The Cauchy-Riemann relations, characteristical and canonical relations, the Bianchi identities and others are examples of identical relations. It can be…

I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such…

It is increasingly widely believed that at high levels of resolution spacetime geometry may be inherently non-commutative. In this work we introduce an effective mechanism that maps matter fields onto a non-commutative background manifold.…

We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…

In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity…

The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the…

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like…

The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…

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.…

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…

Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine…

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…

Differential forms provide a coordinate-free way to express many quantities and relations in mathematical physics. In particular, they are useful in plasma physics. This tutorial gives a guide so that you can read the plasma physics…

The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…

In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure…

This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…

The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space-time models, especially the simplest one, ${\bf R^4}$, possess a rich multiplicity of…

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism \omega…