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https://www.ias.ac.in/article/fulltext/pram/061/05/0949-0953

Non-covariant gauges; interpolating gauges; path-integrals; WT-identities

We discuss the viability of using interpolating gauges to define the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition defining term. We show that the boundary condition needed to maintain gauge-invariance as the interpolating parameter θ varies, depends very sensitively on the parameter variation. We do this with a gauge used by Doust. We also consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. We point out the necessity of inclusion of an ε-term (even) in theformal treatments, without which one may reach incorrect conclusions. We, further, point out that the ε-termcan contribute to the BRST WT-identities in a non-trivial way (even as ε → 0). We point out that these contributions lead to additional constraints on Green's function that arenot normally taken into account in the BRST formalism that ignores the ε-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that a prescription, in general, will require renormalization; if at all it is to be viable.

Satish D Joglekar¹

1. Department of Physics, Indian Institute of Technology, Kanpur - 208 016, India