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The Faddeev-Popov technique in gauge field theories Sharpe, Bruce John


We adapt the Faddeev-Popov technique to lattice gauge field theories. Our formulation strongly suggests that the Faddeev-Popov formula, which has come into doubt since the discovery of Gribov ambiguities, is in fact correct. More precisely, we show that Gribov ambiguities can occur in the lattice theory, but that "usually" they do not affect the Faddeev-Popov formula; a method is given for determining when the lattice Faddeev-Popov formula is not valid. We are able to answer in the lattice theory many questions that arise naturally in the continuum theory but which have remained unsettled up to now. We show that a formal limit of the lattice Faddeev-Popov formula yields the usual continuum formula. We prove some partial results which bear on the problem of proving a rigorous continuum limit.

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