Supersymmetric Canonical Commutation Relations

TL;DR

This paper develops a supersymmetric framework for canonical quantization of various fields, revealing new features in massless vector fields through supersymmetric positivity and Hilbert-Krein structures.

Contribution

It introduces unitarily represented supersymmetric canonical commutation relations for quantizing different fields, highlighting novel aspects in the massless vector case.

Findings

New facets in massless vector fields due to supersymmetry

Use of Hilbert-Krein structure for positivity

Unified quantization approach for chiral, antichiral, and vector fields

Abstract

We present unitarily represented supersymmetric canonical commutation relations which are subsequently used to canonically quantize massive and massless chiral,antichiral and vector fields. The massless fields, especially the vector one, show new facets which do not appear in the non superymmetric case. Our tool is the supersymmetric positivity induced by the Hilbert-Krein structure of the superspace.