Extension of von Neumann's uniqueness theorem to the theories with non-physical particles

TL;DR

This paper extends von Neumann's uniqueness theorem to include anti-Fock representations on Krein spaces, broadening its applicability to theories involving non-physical particles.

Contribution

It introduces an extension of the theorem to a new class of canonical commutation relations realized on Krein spaces, relevant for non-physical particles.

Findings

Extended von Neumann's theorem to anti-Fock representations

Applied theorem to theories with non-physical particles

Demonstrated mathematical consistency on Krein spaces

Abstract

Von Neumann's uniqueness theorem is extended to a special class of canonical commutation relations, namely the anti-Fock representations, which are realized on a Krein space.