On the Hopf algebraic origin of Wick normal-ordering

TL;DR

This paper explores the Hopf algebraic foundations of Wick normal-ordering in quantum field theory, revealing a combinatorial approach that simplifies calculations and provides algebraic expressions.

Contribution

It introduces a Hopf algebraic interpretation of Wick re-ordering, connecting combinatorial formulas to algebraic identities in quantum field theory.

Findings

Wick's theorem is expressed as a Hopf algebraic identity called Cliffordization.

The combinatorial Hopf algebra approach simplifies computations in quantum field theory.

Closed algebraic expressions for Wick re-ordering are derived using Hopf algebra techniques.

Abstract

A combinatorial formula of G.-C. Rota and J.A. Stein is taken to perform Wick re-ordering in quantum field theory. Wick's theorem becomes a Hopf algebraic identity called Cliffordization. The combinatorial method relying on Hopf algebras is highly efficient in computations and yields closed algebraic expressions. AMS Subject Classifications 2000: 81R50; 16W30