Spectral Properties of Wick Power Series of a Free Field with an Indefinite Metric

TL;DR

This paper investigates the spectral properties of Wick power series of a free field with indefinite metric, demonstrating their convergence and spectral conditions within the pseudo-Wightman framework using advanced functional analysis.

Contribution

It extends the spectral analysis of Wick power series to fields with indefinite metrics, employing a generalized Paley-Wiener-Schwartz theorem for the spectral condition.

Findings

Wick power series can converge to fields satisfying pseudo-Wightman axioms.

Spectral conditions are formulated via carrier cones for analytic functionals.

A generalized Paley-Wiener-Schwartz theorem supports the spectral analysis.

Abstract

The properties of infinite series in the Wick powers of a free field whose two-point correlation function has a singular infrared behavior and does not satisfy the positivity condition are investigated. If these series are defined on an appropriate functional domain, then the fields to which they converge satisfy all conditions of the pseudo-Wightman formalism. For series convergent only on analytic test functions in the momentum representation, the spectral condition is formulated using the previously introduced notion of a carrier cone of an analytic functional. A suitable generalization of the Paley-Wiener-Schwartz theorem is used to prove that this condition is satisfied.