Wick theorem for all orderings of canonical operators

Abstract

Wick’s theorem, known for yielding normal ordered from time-ordered bosonic fields, may be generalized for a simple relationship between any two orderings that we define over canonical variables, in a broader sense than before. In this broad class of orderings, the general Wick theorem follows from the Baker–Campbell–Hausdorff identity. We point out that, generally, the characteristic function does not induce an unambigous scheme to order the multiple products of the canonical operators although the value of the ordered product is unique. We construct a manifold of different schemes for each value of s of s-orderings of Cahill and Glauber.