Supersymmetric Distributions, Hilbert Spaces of Supersymmetric Functions and Quantum Fields

TL;DR

This paper explores the mathematical structures of supersymmetric distributions and Hilbert spaces of supersymmetric functions, applying these concepts to address foundational issues in rigorous supersymmetric quantum field theory.

Contribution

It introduces the use of Hilbert-Krein and positivity structures of superspace within superdistributions to advance the mathematical framework of supersymmetric quantum field theory.

Findings

Development of a rigorous mathematical framework for supersymmetric quantum fields

Application of Hilbert-Krein structures to superspace problems

Enhanced understanding of positivity in supersymmetric distributions

Abstract

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.