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arXiv · 1404.4604

Gauge field theories: various mathematical approaches

François Jordan·Lazzarini Serge·Masson Thierry
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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.

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François Jordan, Lazzarini Serge, Masson Thierry. 2014-04-17. Gauge field theories: various mathematical approaches. https://arxiv.org/abs/1404.4604

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