Related papers: The Nonlinear Maxwell Theory---an Outline
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet…
In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM). We are interested to analyse the existence of solitons, namely of finite energy solutions which exhibit stability properties. This paper is divided in two parts. In…
We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
We propose a novel geometric model of three-dimensional topological insulators in presence of an external electromagnetic field. The gapped boundary of these systems supports relativistic quantum Hall states and is described by a…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry.
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.
In the present paper it is shown that the Yang-Mills equation can be represented as the equation of the non-linear electromagnetic waves superposition. The research of the topological characteristics of this representation allows us to…
We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
Starting from the Maxwell's equations and without resort to the paraxial approximation, we derive equations describing stationary (1+1)-dimensional beams propagating at an arbitrary direction in an optical crystal with cubic symmetry and…