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    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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Indefinite Inner Product Spaces

Indefinite Inner Product Spaces

Bognar, J.

Paperback

Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge, Book 78

Algebra

ISBN10: 3642655696
ISBN13: 9783642655692
Publisher: Springer Nature
Published: Nov 11 2011
Pages: 226
Weight: 0.72
Height: 0.51 Width: 6.00 Depth: 9.00
Language: English
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was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics.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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