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Indefinite Inner Product Spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (78)) free ebook download

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Author(s):	J. Bognar

Date:	2011	Format:	djvu	Language:	English	ISBN/ASIN:	3642655696
Pages:	1	OCR:		Quality:		ISBN13:
Uploader:	tvladb77	Upload Date:	4/29/2022 9:15:12 PM

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By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli  on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L.Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.

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Indefinite Inner Product Spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (78)) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics