Turkish Journal of Physics
Product Integral Representations of Wilson Lines and Wilson Loops and Non-Abelian Stokes Theorem
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of Wilson lines and Wilson loops as approximating them with partial sums, their convergence, and their behavior under gauge transformations. We also obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes theorem.
KARP, ROBERT L.; MANSOURI, FREYDOON; and RNO, JUNG S. (2000) "Product Integral Representations of Wilson Lines and Wilson Loops and Non-Abelian Stokes Theorem," Turkish Journal of Physics: Vol. 24: No. 3, Article 17. Available at: https://journals.tubitak.gov.tr/physics/vol24/iss3/17