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Spectral properties of Wick power series for a free field with an indefinite metric

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Abstract

The properties of infinite series in Wick powers of a free field whose two-point correlation function has singular infrared behavior and does not satisfy the positivity condition are investigated. If these series are defined on an appropriate functional domain, then the fields they converge to satisfy all conditions of the pseudo-Wightman formalism. For series convergent only on analytic test functions in the momentum representation, the spectral condition is formulated using the previously introduced notion of the carrier cone of an analytic functional. A suitable generalization of the Paley-Wiener-Schwartz theorem is used to prove that this condition is satisfied.

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References

  1. A. G. Smirnov and M. A. Solov'ev,Theor. Math. Phys.,123, 709 (2000).

    Article  Google Scholar 

  2. N. N. Bogoliubov, A. A. Logunov, A. I. Oksak and I. T. Todorov,General Principles of Quantum field Theory [in Russian], Nauka, Moscow (1987); English transl., Kluwer, Dordrecht (1990).

    Google Scholar 

  3. U. Moschella and F. Strocchi,Lett. Math. Phys.,24, 103 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  4. U. Moschella,J. Math. Phys.,34, 535 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  5. M. A. Soloviev,Theor. Math. Phys.,105, 1520 (1995).

    Article  Google Scholar 

  6. I. M. Gelfand and G. E. Shilov,Generalized Functions [in Russian], Vol. 2,Functions and Generalized Function Spaces, Gos. Izd. Fiz.-Mat. Lit., Moscow (1958); English transl., Acad. Press, New York (1968).

    Google Scholar 

  7. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. 1,Functional Analysis, Acad. Press, New York (1972).

    MATH  Google Scholar 

  8. M. A. Soloviev,Lett. Math. Phys.,33, 49 (1995).

    Article  ADS  Google Scholar 

  9. M. A. Soloviev,Commun. Math. Phys.,184, 579 (1997).

    Article  ADS  Google Scholar 

  10. R. T. Rockafellar,Convex Analysis, Princeton Univ. Press, Princeton, NJ (1970).

    Book  MATH  Google Scholar 

  11. S. Mandelbrojt,Closure Theorems and Composition Theorems [in Russian] (Lectures at Moscow State University transcribed and translated by E. A. Gorin, A. S. Dynin, and B. S. Mityanin and edited using the monographs by S. Mandelbrojt,General Theorems of Closure (Rice Inst. Pamphlet, Spec. issue, Nov. 1951) andComposition Theorems (Rice Inst. Pamphlet,45, 3, Oct. 1958); also includes a translation of the paper by S. Mandelbrojt, “Sur un problème de Gelfand et Shilov”,Ann. Sci. École Norm. Sup.,77, No. 2, 1960)), Izd. Inostr. Lit., Moscow (1962).

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  1. Lebedev Physical Institute, RAS, Moscow, Russia

    A. G. Smirnov & M. A. Solov'ev

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  1. A. G. Smirnov
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  2. M. A. Solov'ev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 57–73, October, 2000.

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Smirnov, A.G., Solov'ev, M.A. Spectral properties of Wick power series for a free field with an indefinite metric. Theor Math Phys 125, 1349–1362 (2000). https://doi.org/10.1007/BF02551041

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