Gauge field theories: various mathematical approaches
Mathematical Physics
2014-04-18 v1 High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.
Cite
@article{arxiv.1404.4604,
title = {Gauge field theories: various mathematical approaches},
author = {François Jordan and Lazzarini Serge and Masson Thierry},
journal= {arXiv preprint arXiv:1404.4604},
year = {2014}
}
Comments
33 pages. To be published in the book: Mathematical Structures of the Universe (Copernicus Center Press, Krak\'ow, Poland, 2014)