The Geometrical Basis of the Nonlinear Gauge

Details The Geometrical Basis of the Nonlinear Gauge The Geometrical Basis of the Nonlinear Gauge

2001-10-04

arxiv.org/abs/hep-th/0110038v2

Physics

High Energy Physics

High Energy Physics - Theory

3 figures, 19 pages

Scientific paper

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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