Quantum-field theories as representations of a single $^\ast$-algebra

TL;DR

This paper demonstrates that various quantum field theories can be unified as representations of a single $^\ ext{ast}$-algebra, providing a rigorous framework for their approximation and continuum limits.

Contribution

It introduces a unified algebraic framework for multiple quantum field theories and rigorously defines their lattice approximations and continuum limits.

Findings

Quantum field theories are representations of a single $^\ ext{ast}$-algebra.

The paper provides a rigorous definition of the continuum limit.

Lattice approximations of these theories are proven to exist.

Abstract

We show that many well-known quantum field theories emerge as representations of a single $^\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field theories, and string theories. We prove that such theories can be approximated on lattices, and we give a rigorous definition of the continuum limit of lattice quantum field theories.