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Some Observations on Non-covariant Gauges and the epsilon-term

Satish D. Joglekar
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Abstract

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an epsilon-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the epsilon-term can contribute to the BRST WT-identities in a nontrivial way (even as epsilon-->0). We also show that the (expectation value of the) correct epsilon-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic epsilon -term, that they lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism that ignores the epsilon-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.

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Satish D. Joglekar. 2002-05-06. Some Observations on Non-covariant Gauges and the epsilon-term. https://doi.org/10.1142/s0217732302009192

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