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Yang-Mills fields as optical media

R. Aldrovandi·A. L. Barbosa
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Abstract

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be looked at from a new point of view. The Wu-Yang ambiguity, for example, appears related to the multiple possible torsions of distinct metric-preserving connections. In a second step, also the ambient space becomes curved. In general, the strictly Riemannian, metric sector plays the role of an arbitrary host space, with the gauge field represented by a contorsion. For some field configurations, however, it is possible to obtain a purely metric representation. In those cases, if the space is symmetric homogeneous the Christoffel connections are automatically solutions of the Yang-Mills equations.

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R. Aldrovandi, A. L. Barbosa. 2001-07-27. Yang-Mills fields as optical media. https://arxiv.org/abs/math-ph/0107027

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