On Bosonic Wightman Quantum Field Theories

TL;DR

This paper proves that bosonic Wightman quantum field theories with CCRs have a unique algebraic structure derived from their two-point functions, ensuring well-defined self-adjoint field operators.

Contribution

It establishes the existence of Weyl CCRs and the unique C*-algebra structure for bosonic Wightman fields based on their two-point functions.

Findings

Field operators have self-adjoint extensions

Weyl CCRs exist for bosonic fields obeying CCRs

The CCR algebra is uniquely determined by the two-point function

Abstract

We prove that field operators in a Wightman quantum field theory generally have self-adjoint extensions. If the theory is bosonic and the field operators also obey canonical commutation relations (CCRs), then the Weyl form of the CCRs exits. This entails that the field operators emerge from the corresponding CCR algebra, which is a unique C$^\ast$-algebra and which is determined by the two-point Wightman function.