Related papers: Geometrization of Classical Wave Fields
The analysis of wave patterns in a structure which possesses periodicity in the spatial and temporal dimensions is presented. The topic of imperfect chiral interfaces is also considered. Although causality is fundamental for physical…
Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation,…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…
Multiple potential wells for massive test particles, allowing distinct families of bound orbits to coexist, are a characteristic feature of certain exotic compact objects beyond general relativity. Taking the dyonic black hole as a…
We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry…
Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal…
Predictive theory to geometrically engineer devices and materials in continuum systems to have desired topological-like effects is developed here by bridging the gap between quantum and continuum mechanical descriptions. A platonic crystal,…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…
The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although glasses are also solids, their structure resembles closely the one of a liquid and…
The problem about geometric correspondence of Dirac particle and contain quality item of Yang-Mills equation has always not been solved.This paper introduced the hyperbolic imaginary unit in Minkowski space, established a classes of Dirac…
As a point of departure it is suggested that Quantum Cosmology is a topological concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
We characterise the particlelike kinematics of charge-carrying topological defects in nematic media via a geometric field theory. This differs from the theory of electromagnetism, with which it is often compared, due to the absence of…
A model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field…
We propose that particles are associated both with localized macroscopic states at point vertices and with extended microscopic states at all vacuum points. The self-fields screen the microscopic particle currents everywhere except at the…
The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include media with isotropic, inhomogeneous, chirality. It is found that such media may be described through introducing the…