Abstract
We show that the set of solutions of Yang-Mills equations in the Minkowski space-time, with the Cauchy data A ∈ Hk+1(ℝ3), E ∈ Hk (ℝ3), k ≥ 3, is a smooth principal fibre bundle over the reduced phase space with structure group consisting of the gauge symmetries approaching the identity at infinity.
Résumé
Nous démontrons que l’ensemble des solutions de les équations de Yang-Mills dans l’espace-temps de Minkowski, pour les données de Cauchy A ∈ Hk+1(ℝ3), E ∈ Hk(ℝ3), k ≥ 3, est un espace fibré ayant pour base l’espace de phase reduit et pour groupe structural le groupe de symétries de jauge approchant l’identité à l’infini.
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Śniatycki, J. (2003). Geometry of Solution Spaces of Spaces of Yang-Mills Equations. In: de Gosson, M. (eds) Jean Leray ’99 Conference Proceedings. Mathematical Physics Studies, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2008-3_18
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DOI: https://doi.org/10.1007/978-94-017-2008-3_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6316-8
Online ISBN: 978-94-017-2008-3
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