Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 4

Multisymplectic formulation of Yang–Mills equations and Ehresmann connections

Pages: 805 – 835

DOI: http://dx.doi.org/10.4310/ATMP.2015.v19.n4.a4

Author

Frédéric Hélein (Institut de Mathématiques de Jussieu, Université Denis Diderot, Paris, France)

Abstract

We present a multisymplectic formulation of the Yang–Mills equations. The connections are represented by normalized equivariant $1$-forms on the total space of a principal bundle, with values in a Lie algebra. Within the multisymplectic framework we realize that, under reasonable hypotheses, it is not necessary to assume the equivariance condition a priori, since this condition is a consequence of the dynamical equations.

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Published 20 January 2016