New Examples for Wightman Fields on a Manifold

TL;DR

This paper demonstrates that the product of two free scalar fields on a manifold forms a well-defined operator valued distribution, providing a new example of a Wightman field on a manifold with all n-point distributions existing.

Contribution

It introduces a novel construction of Wightman fields on manifolds by establishing the well-defined nature of the product of free scalar fields as an operator valued distribution.

Findings

Product of two free scalar fields is a well-defined operator valued distribution.

All n-point distributions for the new field exist.

Provides a new example of a Wightman field on a manifold.

Abstract

The product of two free scalar fields on a manifold is shown to be a well defined operator valued distribution on the GNS Hilbert space of a globally Hadamard product state. Viewed as a new field all n-point distributions exist, giving a new example for a Wightman field on a manifold.