TL;DR
This paper develops the mathematical framework of super Hilbert spaces over Grassmann algebras, which are relevant in the functional Schrödinger representation of spinor quantum field theory.
Contribution
It formulates the foundational structure of super Hilbert spaces over Grassmann algebras, extending the mathematical tools for quantum field theory.
Findings
Framework for super Hilbert spaces over Grassmann algebras established
Application to spinor quantum field theory demonstrated
Mathematical properties of Grassmann-valued inner products analyzed
Abstract
The basic mathematical framework for super Hilbert spaces over a Grassmann algebra with a Grassmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Grassmann algebras arise in the functional Schroedinger representation of spinor quantum field theory in a natural way.
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