Loop approaches to gauge field theory

Abstract

Basic mathematical and physical concepts in loop- and path-dependent formulations of Yang-MiIls theory are reviewed and set into correspondence. We point out some problems peculiar to these non-local approaches, in particular those associated with defining structure on various kinds of loop spaces. The issues of classical loop equations, differential operators, lattice gauge theory, loop algebras, and canonical quantization are discussed in some detail, and the paper concludes with an extensive list of references.