Test Function Space for Wick Power Series

TL;DR

This paper establishes a criterion for the test function space enabling the operator realization of Wick power series in quantum field theory, applicable even in gauge theories with indefinite metrics.

Contribution

It introduces a new criterion for test function spaces that does not rely on positive metric assumptions, broadening applicability to gauge theories.

Findings

Provides a practical criterion for test function spaces

Applicable to gauge theories with indefinite metrics

Uses analytic properties of Hilbert majorant

Abstract

We derive a criterion that is convenient for applications and exactly characterizes the test function space on which the operator realization of a given series of Wick powers of a free field is possible. The suggested derivation does not use the assumption that the metric of the state space is positive and can therefore be used in a gauge theory. It is based on the systematic use of the analytic properties of the Hilbert majorant of the indefinite metric and on the application of a suitable theorem on the unconditional convergence of series of boundary values of analytic functions.