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BRS and anti-BRS symmetries in the planar gauge
Phys. Rev. D 38, 2579 – Published 15 October, 1988
DOI: https://doi.org/10.1103/PhysRevD.38.2579
Abstract
The planar gauge is reexamined from various points of view. First, we find an annoying ambiguity in the definition of the product of two propagators. Second, Becchi-Rouet-Stora (BRS) invariance can be implemented only at the price of unavoidable second-order derivatives in the Lagrangian. BRS and anti-BRS symmetries cannot be realized simultaneously. If, instead of BRS, anti-BRS symmetry is implemented, the ambiguity does not give rise to different results. There is some simplification in the calculation but the gluon self-energy is neither conserved nor orthogonal to n. Again, second-order derivatives are unavoidable in the invariant Lagrangian. For all these reasons, the planar gauge with its usual propagator either with BRS or with anti-BRS symmetry does not seem to be a true gauge for Yang-Mills theory.
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