Canonical methods in non-Abelian gauge theories

The exploitation of unrenormalized canonical field equations and equal-time commutation relations is generally not fruitful because of the need for infinite renormalization. The asymptotically free non-Abelian gauge theories are much more benign in their ultraviolet behavior. Under certain smoothness assumptions, canonical methods applied to the A/sup a//sub μ/(x) A/sup b//sub ν/(0) operator-product expansion are shown to lead to information on the exact singularity structure of the theory. As a result, we show (1) that the unrenormalized gauge coupling constant g0(K) as a function of the cutoff K has the behavior g0(K) approx. (lnK)-1/2, (2) how to renormalize a/sup μ/ x a/sup ν/ (where a/sup μ/ is the unrenormalized gauge field), and (3) that the field-strength tensor partial/sup μ/a/sup μ/ - partial/sup ν/a/sup μ/ + g0a/sup μ/ x a/sup ν/ becomes proportional to F/sup μ//sup ν/ = partial/sup μ/A/sup ν/ - partial/sup ν/A/sup μ/ upon renormalization. These conclusions agree with results obtained by the use of renormalization-group equations