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

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.Comment: 12 pages, LaTeX2

Absence of Nonlocal Counter-terms in the Gauge Boson Propagator in Axial -type Gauges

We study the two-point function for the gauge boson in the axial-type gauges. We use the exact treatment of the axial gauges recently proposed that is intrinsically compatible with the Lorentz type gauges in the path-integral formulation and has been arrived at from this connection and which is a ``one-vector'' treatment. We find that in this treatment, we can evaluate the two-point functions without imposing any additional interpretation on the axial gauge 1/(n.q)^p-type poles. The calculations are as easy as the other treatments based on other known prescriptions. Unlike the ``uniform-prescription'' /L-M prescription, we note, here, the absence of any non-local divergences in the 2-point proper vertex. We correlate our calculation with that for the Cauchy Principal Value prescription and find from this comparison that the 2-point proper vertex differs from the CPV calculation only by finite terms. For simplicity of treatment, the divergences have been calculated here with n^2>0 and these have a smooth light cone limit.Comment: 17 pages; 3 figures drawn using feyn.st