Definite and Indefinite Inner Product on Superspace (Hilbert-Krein Superspace)
Florin Constantinescu
TL;DR
This paper introduces natural scalar products with definite and indefinite signatures on N=1 superspace, revealing an inherent Hilbert-Krein structure, motivated by supersymmetry but grounded in a general mathematical framework.
Contribution
It establishes a mathematical framework for scalar products on superspace that exhibit Hilbert-Krein structure, bridging physics motivation with rigorous mathematics.
Findings
Superspace admits invariant scalar products with definite and indefinite signatures.
The scalar products induce a Hilbert-Krein structure on superspace.
The framework is general and not limited to specific physical models.
Abstract
We present natural (invariant) definite and indefinite scalar products on the N=1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical framework.
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