A Note on the Real Fermionic and Bosonic quadratic forms: Their Diagonalization and Topological Interpreation

We explain in this note how real fermionic and bosonic quadratic forms can be effectively diagonalized. Nothing like that exists for the general complex hermitian forms. Looks like this observation was missed in the Quantum Field theoretical literature. The present author observed it for the case of...

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Bibliographic Details
Published inarXiv.org
Main Author Novikov, Sergey P
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.10.2001
Subjects
Fermions
Fields (mathematics)
Quadratic forms
Topology
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Summary:We explain in this note how real fermionic and bosonic quadratic forms can be effectively diagonalized. Nothing like that exists for the general complex hermitian forms. Looks like this observation was missed in the Quantum Field theoretical literature. The present author observed it for the case of fermions in 1986 making some topological work dedicated to the problem: how to construct Morse-type inequalities for the generic real vector fields? This idea also is presented in the note.
ISSN:2331-8422