Open AccessSupersymmetric Hilbert space.
Author(s) -
GianCarlo Rota,
Joël Stein
Publication year - 1990
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.87.2.653
Subject(s) - symmetric bilinear form , mathematics , hilbert space , bilinear form , generalization , corollary , vector space , pure mathematics , dual space , invariant (physics) , space (punctuation) , extension (predicate logic) , basis (linear algebra) , algebra over a field , mathematical analysis , mathematical physics , computer science , geometry , programming language , operating system
A generalization is given of the notion of a symmetric bilinear form over a vector space, which includes variables of positive and negative signature ("supersymmetric variables"). It is shown that this structure is substantially isomorphic to the exterior algebra of a vector space. A supersymmetric extension of the second fundamental theorem of invariant theory is obtained as a corollary. The main technique is a supersymmetric extension of the standard basis theorem. As a byproduct, it is shown that supersymmetric Hilbert space and supersymplectic space are in natural duality.