Another Formulation of the Wick's Theorem. Farewell, Pairing?

TL;DR

This paper introduces an algebraic formulation of Wick's theorem that expresses vacuum and thermal averages as determinants or permanents of matrices, simplifying calculations in quantum field theory and statistical physics.

Contribution

It presents a new algebraic approach to Wick's theorem that facilitates practical computations using symbolic mathematics and computer algebra systems.

Findings

Allows vacuum and thermal averages to be written as determinants or permanents

Simplifies calculations in quantum field theory and statistical physics

Enhances computational efficiency with symbolic mathematics

Abstract

The algebraic formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each element of the matrix is the average of the chronological product of only two operators. This formulation is extremely convenient for practical calculations in quantum field theory and statistical physics by the methods of symbolic mathematics using computers.