Towards a Generalized Distribution Formalism for Gauge Quantum Fields

TL;DR

This paper develops a distribution formalism on Gelfand-Shilov spaces that can handle highly singular quantum fields, providing tools for consistent treatment of fields with extreme ultraviolet and infrared behaviors.

Contribution

It proves that distributions on Gelfand-Shilov spaces have uniquely determined support cones, enabling advanced distribution-theoretic techniques for quantum field analysis.

Findings

Distributions on Gelfand-Shilov spaces retain angular localizability.

Support cones are uniquely determined for these distributions.

The framework applies to quantum fields with extreme singularities.

Abstract

We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic techniques suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proofs covering the most general case are based on the use of the theory of plurisubharmonic functions and Hormander's estimates.