New Gauge Invariant Variables for Yang-Mills Theory

Details New Gauge Invariant Variables for Yang-Mills Theory New Gauge Invariant Variables for Yang-Mills Theory

1995-05-31

arxiv.org/abs/hep-th/9505188v1

Physics

High Energy Physics

High Energy Physics - Theory

9pp., LaTeX

Scientific paper

A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance found to hold for the basic equations and commutators of the theory in the canonical formalism. We emphasize, however, that we are not interested in and do not consider the coupling of the theory to gravity. We concentrate here on a technical difficulty of this approach, the calculation of the electric field energy. This in turn hinges on the well-definedness of the transformation of variables, an issue which is settled through degenerate perturbation theory arguments.

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