[PDF][PDF] Gauge field theories: various mathematical approaches
J François, S Lazzarini, T Masson - arXiv preprint arXiv …, 2014 - researchgate.net
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 …
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 …
Gauge field theories: various mathematical approaches
F Jordan, L Serge, M Thierry - arXiv preprint arXiv:1404.4604, 2014 - arxiv.org
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 …
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 …