2,252 research outputs found
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
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
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