On the reconstruction of the physical Hilbert spaces for quantum field theories with indefinite metric

Abstract

It is known that there may exist one or more Hilbert space structures corresponding to an indefinite metric quantum field theory. In this paper we prove that: (a) the existence of a Hilbert space structure is not needed in the construction of the physical Hilbert space(s); (b) different choices of the Hilbert space structure lead to physical Hilbert spaces isomorphic to that (those) mentioned in (a). Consequently, the physical content of the theory can be read off directly from the Wightman functions—in perfect analogy with the positive metric case. In this light we discuss a weaker form of the Wightman–Gårding–Strocchi axioms for indefinite metric quantum field theories.