Loop approaches to gauge field theories

Basic mathematical and physical concepts in loop- and path-dependent formulations of Yang–Mills 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 concludeswith an extensive list of references.