The continuity of the gauge fixing condition n⋅∂n⋅A=0

To investigate the continuity of the gauge condition n⋅∂n⋅A=0, the continuity of generators of Wilson lines is studied here in the frame of non-Abelian gauge theory in the space R⨂S1⨂S1⨂S1, which guarantees the continuity of the gauge condition n⋅∂n⋅A=0 as proved in our previous work. Starting from SU(2) theory, it is proved that the gauge fixing condition is continuous in a compact subspace of R⨂S1⨂S1⨂S1 given that gauge potentials are differentiable with continuous derivatives. For continuous SU(2) gauge potentials in the space R⨂S1⨂S1⨂S1 that satisfy suitable boundary conditions, which is topologically equivalent to continuous gauge potentials in a compact space, the gauge fixing condition n⋅∂n⋅A=0 is proved to be continuous given that gauge potentials are differentiable with continuous derivatives. The conclusion is extended to the case that lengths along all directions of the space tend to ∞. Lorentz invariance is restored in this limit for quantities which are multiplicative renormalized and free from possible singularities in functional integrals. The same conclusion is proved for general SU(Nc) theory.

Abstract licence: CC BY

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