Super Hilbert Spaces
Copyright policy )Super Hilbert Spaces
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.
Version for Communication in Mathematical Physics; several typos corrected and one example rewritten and expanded
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General theory of differentiable manifolds, Functional analysis on superspaces (supermanifolds) or graded spaces, Path integrals in quantum mechanics, Generalizations of inner products (semi-inner products, partial inner products, etc.), Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), super Hilbert space, FOS: Physical sciences, Mathematical Physics (math-ph), spinor quantum field theory, weakly selfadjoint operator, \(C^*\)-modules, Hilbert module, observable, Graßmann algebra, Mathematical Physics, Schrödinger representation
General theory of differentiable manifolds, Functional analysis on superspaces (supermanifolds) or graded spaces, Path integrals in quantum mechanics, Generalizations of inner products (semi-inner products, partial inner products, etc.), Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), super Hilbert space, FOS: Physical sciences, Mathematical Physics (math-ph), spinor quantum field theory, weakly selfadjoint operator, \(C^*\)-modules, Hilbert module, observable, Graßmann algebra, Mathematical Physics, Schrödinger representation
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