Related papers: Line geometry and electromagnetism I: basic struct…
I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in…
The standard description of particles and fundamental interactions is crucially based on a regular metric background. In the language of differential geometry, this dependence is encoded into the action via Hodge star dualization. As a…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
A description of electromagnetism as four-dimensional spacetime structure leads to the dynamics of a charged particle being determined only by the four-vector potential and the existence of an electromagnetic field depending on the…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
We compare the nature of electromagnetic fields and of gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular the "lines of force" visualizations of…
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…
This survey is meant to provide an introduction to the fundamental theorem of linear algebra and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to linear algebra. Specifically, we…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
In the previous papers (/quant-ph/0204037, /quant-ph/0204134, quant-ph/0205075), based on Dirac's equation we have considered the electromagnetic structure of the leptons. In the present paper, using the Yang-Mills equation we will analyse…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
These are six papers joined by the same title. The main topics are: 1. algebraic nature of quantization of relativistic fields, 2. constructive definition of space of states of quantum electromagnetic field, 3. structure of space of states…
This is the second in a series of papers intended to provide a basic overview of some of the major ideas in particle physics. Part I [arXiv:0810.3328] was primarily an algebraic exposition of gauge theories. We developed the group theoretic…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…
How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time and distance, critical speed which spinning…