Construction of envelopes of holomorphy and QFT

TL;DR

This paper explores the extension of holomorphic functions within quantum field theory, revealing non-restrictedness properties in mass gap scenarios, and advances understanding of complex analysis in QFT contexts.

Contribution

It introduces new methods for continuing holomorphic functions in QFT, specifically addressing mass gap situations and their impact on the structure of holomorphy envelopes.

Findings

Identifies non-restrictedness properties in mass gap cases

Develops new techniques for holomorphic continuation in QFT

Provides results linking holomorphy to spectral properties

Abstract

Methods of continuation of holomorphic functions of several complex variables are investigated within the axiomatic framework of Araki, Haag, and Kastler in local quantum field theory. The motivation comes from the analysis of a mass gap in an energy-momentum spectrum without vacuum vector. The main conclusion is some non-restrictedness property in a mass gap situation. Prior to that, some results on holomorphic functions related to a mass-gap-situation are obtained and investigated.