Wick theorem for all orderings of canonical operators

TL;DR

This paper generalizes Wick's theorem to all orderings of canonical operators, establishing a broad framework that includes various ordering schemes and derives from the Baker-Campbell-Hausdorff identity.

Contribution

It introduces a generalized Wick theorem applicable to any ordering of canonical operators, expanding the theoretical understanding of operator orderings beyond traditional methods.

Findings

Derived a broad class of orderings using the Baker-Campbell-Hausdorff identity.

Constructed a manifold of schemes for s-orderings of Cahill and Glauber.

Clarified the relationship between characteristic functions and operator orderings.

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 (GWT) follows from the Baker-Campbell-Hausdorff identity. We point out that, generally, the characteristic function does not induce an unambiguous 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.