An Algebraic Proof of Thermal Wick's Theorem

TL;DR

This paper provides an algebraic proof of thermal Wick's theorem, demonstrating how thermal expectations can be expressed as sums of vacuum expectations, simplifying calculations in many-body quantum systems.

Contribution

It introduces an algebraic approach to prove thermal Wick's theorem, offering a new perspective on thermal expectation calculations in many-body physics.

Findings

Thermal expectation values can be transformed into vacuum expectation sums.

The algebraic proof simplifies the application of Wick's theorem at finite temperature.

The approach broadens understanding of many-body state constructions.

Abstract

Every many-body state can be constructed from the vacuum state by iteratively applying the creation operators, therefore the thermal expectation can be transformed into a sum of vacuum expectation where the vacuum Wick's theorem holds. Based on this observation this article gives an algebraic proof of thermal Wick's theorem.