Indefinite Inner Product Spaces

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  • Indefinite Inner Product Spaces Book Detail

  • Author : J. Bognar
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 235
  • ISBN 13 : 364265567X
  • File Size : 58,58 MB

Indefinite Inner Product Spaces by J. Bognar PDF Summary

Book Description: 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was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics.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

Indefinite Inner Product Spaces

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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 pre

Operator Theory in Inner Product Spaces

Operator Theory in Inner Product Spaces

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This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, held at the TU Berlin, Germa