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Analogue of the Weyl representation of algebra of canonical commutation relations in the case of nonphysical particles

  • Physics of Elementary Particles and Atomic Nuclei. Theory
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Abstract

An analogue of the Weyl representation of the algebra of canonical commutation relations is proved to exist in the anti-Fock case achieved in Krein space.

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References

  1. T. Kugo and I. Ojima, Suppl. Prog. Theor. Phys. 66, 1 (1979).

    Article  ADS  Google Scholar 

  2. G. Morchio and F. Strocchi, Ann. Inst. H. Poincaré A 33, 251 (1980).

    MathSciNet  Google Scholar 

  3. C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics (Springer-Verlag, Berlin, Heidelberg, New York, 1967), Ch. 4, p. 63.

    Google Scholar 

  4. K. Yosida, Functional Analysis, Springer Classics in Mathematics (Springer, New York, 1996; Mir, Moscow, 1967).

    Google Scholar 

  5. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics (Springer-Verlag, Berlin, Heidelberg, New York, 1979), Vol. 2.

    MATH  Google Scholar 

  6. C. Foias, L. L. Geher, and B. Sz.-Nagy, Acta Sec. Math. (Szeged) 21, 78 (1960).

    MathSciNet  MATH  Google Scholar 

  7. Yu. S. Vernov, M. N. Mnatsakanova, and S. G. Salynskii, “A New Definition of Regularity for Representation of Canonical Commutation Relations Algebras,” Mosc. Univ. Phys. Bull. 65, 547 (2010).

    Article  ADS  Google Scholar 

  8. J. Bognar, Indefinite Inner Product Spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1974).

    MATH  Google Scholar 

  9. T. Ya. Azizov and I. S. Iokhvidov, Foundations of the Theory of Linear Iperators in Spaces with Indefinite Metric (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  10. M. G. Krein, Am. Math. Soc. Transl. 93, 103 (1970).

    MathSciNet  Google Scholar 

  11. M. Mnatsakanova et al., J. Math. Phys. 39, 2969 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Original Russian Text © Yu.S. Vernov, M.N. Mnatsakanova, S.G. Salynskii, 2012, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2012, No. 3(173), pp. 353–358.

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Vernov, Y.S., Mnatsakanova, M.N. & Salynskii, S.G. Analogue of the Weyl representation of algebra of canonical commutation relations in the case of nonphysical particles. Phys. Part. Nuclei Lett. 9, 213–215 (2012). https://doi.org/10.1134/S1547477112030132

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  • DOI: https://doi.org/10.1134/S1547477112030132

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