Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-11
Phys.Lett. B619 (2005) 377-386
Physics
High Energy Physics
High Energy Physics - Theory
11pages, 1 figure; abstract, conclusion and discussion are modified related to Gribov copies, typo corrected
Scientific paper
10.1016/j.physletb.2005.06.010
We give a formal proof that the space-time average of the vacuum condensate of mass dimension two, i.e., the vacuum expectation value of the squared potential $\mathscr{A}_\mu^2$, is gauge invariant in the weak sense that it is independent of the gauge-fixing condition adopted in quantizing the Yang-Mills theory. This is shown at least for the small deformation from the generalized Lorentz and the modified Maximal Abelian gauge in the naive continuum formulation neglecting Gribov copies. This suggests that the numerical value of the condensate could be the same no matter what gauge-fixing conditions for choosing the representative from the gauge orbit are adopted to measure it. Finally, we discuss how this argument should be modified when the Gribov copies exist.
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