Product Integrals and Wilson Loops

Wilson loops provide a convenient method of obtaining gauge invariant observables from lattices to strings. On the other hand the product integral formalism was developed in connection with matrix valued differential equations, having built in the feature of order of the matrices. Consequently these come quite handy when dealing with path ordered quantities. As the theory of product integrals is well founded, we can use the various results in the subject to study Wilson lines and loops. In this paper we review the mathematics of the formalism of product integrals and its applications to the physics of Wilson lines and Wilson loops.