Models of local relativistic quantum fields with indefinite metric (in all dimensions)

TL;DR

This paper develops a framework for constructing relativistic quantum field models with indefinite metrics across all dimensions, using truncated Wightman functions derived from Euclidean random fields.

Contribution

It formulates a new condition on truncated Wightman functions that enables the construction of indefinite metric quantum field models in any dimension.

Findings

Models constructed in dimension 4 for vector fields.

Scalar models constructed in all dimensions.

Conditions satisfied by truncated Wightman functions from Euclidean fields.

Abstract

A condition on a set of truncated Wightman functions is formulated and shown to permit the construction of the Hilbert space structure included in the Morchio--Strocchi modified Wightman axioms. The truncated Wightman functions which are obtained by analytic continuation of the (truncated) Schwinger functions of Euclidean scalar random fields and covariant vector (quaternionic) random fields constructed via convoluted generalized white noise, are then shown to satisfy this condition. As a consequence such random fields provide relativistic models for indefinite metric quantum field theory, in dimension 4 (vector case), respectively in all dimensions (scalar case).