Without <gauge fixing>, every <gauge orbit> is integrated infinitely many times and the quadratic gauge-field operator has a <zero mode in field theory> for every pure-gauge direction. It therefore has no inverse and no propagator. A gauge condition selects one representative per orbit, up to global transformations and the possible nonperturbative <Gribov ambiguity>, and makes perturbative Gaussian integration well defined.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 304 / 4 / d / i / Solution

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The Gribov ambiguity is the nonperturbative failure of a local gauge condition to intersect every gauge orbit exactly once. Distinct gauge-equivalent fields satisfying the same condition are Gribov copies.


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