Causal Lie products of free fields and the emergence of quantum field theory

TL;DR

This paper characterizes all causal Lie products for solutions of fundamental equations in Minkowski space, providing insights into the algebraic foundations of quantum field theory.

Contribution

It explicitly determines all causal Lie products of solutions to Klein-Gordon and wave equations, revealing their role in the algebraic structure of quantum field theory.

Findings

All causal Lie products of solutions are classified.

The results illuminate the algebraic origins of quantum field theory.

Provides a comprehensive mathematical framework for causal Lie products.

Abstract

All causal Lie products of solutions of the Klein-Gordon equation and the wave equation in Minkowski space are determined. The results shed light on the origin of the algebraic structures underlying quantum field theory.