Covariant Description of Canonical formalism in Geometrical Theories

Abstract: Quantum field theories are usually studied either by means of path integrals or by means of canonical quantization. Path integral quantization has teh grate virtue of explicitly maintaining all relevant symmetries, such as Poincare invariance. The canonical approach is usually interpreted as an approach that ruins Poincare invariance from the beginning through an explicit choice of a 'time' coordinate. This is not necessarily so, however. The essence of the canonical formalism can be developed in a way that manifestly preserves all relevant symmetries, including Poincare invariance (Witten, 1986; Zuckerman, 1986). The purpose of the present paper is to carry this out in the case of non-abelian gauge theories and general relativity. (link to pdf)