相关论文: Exterior Differential Forms in Field Theory
Within the framework of generalized free field theory at nonzero temperature we address the problem of current conservation. The formalism of thermo field dynamics is used to derive a conserved and thermodynamically consistent physical…
From the equations of conservation laws for energy, linear momentum, angular momentum and mass the evolutionary relation in differential forms follows. This relation connects the differential of entropy and the skew-symmetric form, whose…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the \emph{cognoscenti} of differential forms on manifolds; namely, that charge conservation…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is…
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…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
In the framework of a geometrical model, in which the affine connection of a space is expressed in terms of the electromagnetic field, a possibility of the momentum non-conservation is shown. A toy device with an object moving in a magnetic…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations $\partial\bar\partial\phi_i=-v_i(\bphi)$ for a multicomponent field $\bphi$. Under the assumptions that…
We explore several notions of $k$-form at a point in a diffeological space, construct bundles of such $k$-forms, and compare sections of these bundles to differential forms. As they are defined locally, our $k$-forms can contain more…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
We discuss materials which owe their stability to external fields. These include: 1) external electric or magnetic fields, and 2) quantum vacuum fluctuations in these fields induced by suitable boundary conditions (the Casimir effect).…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…