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arXiv · 1903.00443

Structure of Gauge-Invariant Lagrangians

Marco Castrillón López·Jaime Muñoz Masqué·Eugenia Rosado María
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Abstract

The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of gauge-invariant Lagrangians and how to compute them. More precisely, if $p\colon C\to M$ is the bundle of connections on a principal $G$-bundle $\pi\colon P\to M$, then a finite number $L_1,\dotsc,L_{N^\prime }$ of gauge-invariant Lagrangians defined on $J^1C$ is proved to exist such that for any other gauge-invariant Lagrangian $L\in C^\infty (J^1C)$ there exists a function $F\in C^\infty (\mathbb{R}^{N^\prime })$ such that $L=F(L_1,\dotsc,L_{N^\prime})$. Several examples are dealt with explicitly.

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Marco Castrillón López, Jaime Muñoz Masqué, Eugenia Rosado María. 2019-03-01. Structure of Gauge-Invariant Lagrangians. https://arxiv.org/abs/1903.00443

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