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arXiv · hep-th/0110038

The Geometrical Basis of the Nonlinear Gauge

Jose A. Magpantay
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Abstract

We consider Yang-Mills theory in Euclidean space-time $(R^4)$ and construct its configuration space. The orbits are first shown to form a congruence set. Then we discuss the orthogonal gauge condition in Abelian theory and show that Coulomb-like surfaces foliate the entire configuration space. In the non-Abelian case, where these exists no global orthogonal gauge, we derive the non-linear gauge proposed previously by the author by modifying the orthogonality condition. However, unlike the Abelian case, the entire configuration space cannot be foliated by submanifolds defined by the non-linear gauge. The foliation is only limited to the non-perturbative regime of Yang-Mills theory.

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Jose A. Magpantay. 2003-07-17. The Geometrical Basis of the Nonlinear Gauge. https://arxiv.org/abs/hep-th/0110038

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