Haag's Theorem in the Theories with Non-physical Particles

TL;DR

This paper extends Haag's theorem to quantum field theories formulated in non-degenerate indefinite inner product spaces, broadening its applicability beyond traditional positive-definite frameworks.

Contribution

It introduces a generalized version of Haag's theorem applicable to theories with non-physical particles in indefinite inner spaces.

Findings

Haag's theorem successfully extended to indefinite inner product spaces.

Provides mathematical framework for non-physical particle theories.

Enhances understanding of quantum field theories with indefinite metrics.

Abstract

Haag's theorem is extended to the case of regular representations of the canonical commutation relations in a non-degenerate indefinite inner product space.