General Computations Without Fixing the Gauge

Abstract

Within the framework of a manifestly gauge invariant exact renormalization group for SU(N) Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula by computing the O(g^2) correction to the rectangular, Euclidean Wilson loop with sides T >> L. The standard result is trivially obtained, directly in the continuum, for the first time without fixing the gauge. We comment on possible future applications of the formalism.

11 pages, 5 figures. v2: published in prd, review of methodology shortened, refs added, reformatted

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• Background independent exact renormalisation
• Universality From Very General Nonperturbative Flow Equations in QCD
• A Resummable beta-Function for Massless QED
• Conformal anomaly from gauge fields without gauge fixing
• Properties of a proposed background independent exact renormalization group
• An Extension of Pohlmeyer's Theorem
• Renormalizability of the dimension two gluon operator $A^2$ in a class of nonlinear covariant gauges
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• Ground-state wave-functional in (2+1)-dimensional Yang-Mills theory: Abelian limit, spectrum and robustness