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Nonlocalizability and asymptotical commutativity

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Abstract

The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of a support cone is introduced, which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces Sβ, where 0<β<1. This result leads to a refinement of previous generalizations of the local commutativity condition to nonlocal quantum fields. For string propagators, a new derivation of a representation similar to that of Källen-Lehmann is proposed. It is applicable to any initial and final string configurations and manifests exponential growth of spectral densities intrinsic in nonlocalizable theories.

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References

  1. Gross D.J., Mende P.F., Nucl. Phys.B 303 (1988), 407.

    Google Scholar 

  2. Atick J.J., Witten E., Nucl. Phys.B 310 (1988), 291.

    Google Scholar 

  3. Amati D., Ciafaloni M., Veneziano G., Phys. Lett.B 216 (1989), 41.

    Google Scholar 

  4. Fainberg V.Ya., Marshakov A.V., Phys. Lett.B 211 (1988), 82; Proc. Lebedev Phys. Inst.201 (1990), 139.

    Google Scholar 

  5. Marshakov A.V., Nucl. Phys.B 312 (1989), 178.

    Google Scholar 

  6. Meiman N.N., Sov. Phys. JETP.20 (1965), 1320.

    Google Scholar 

  7. Bümmerstede J., Lücke W., Commun. Math. Phys.37 (1974), 121.

    Google Scholar 

  8. Iofa M.Z., Fainberg V.Ya., Nuovo Cim.A 5 (1971), 273.

    Google Scholar 

  9. Fainberg V.Ya., Soloviev M.A., Ann. Phys.113 (1978), 421.

    Google Scholar 

  10. Iofa M.Z., Fainberg V.Ya., Sov. Phys. JETP.29 (1969), 880.

    Google Scholar 

  11. Iofa M.Z., Fainberg V.Ya., Theor. Math. Phys.11 (1969), 143.

    Google Scholar 

  12. Fainberg V.Ya., Problems of Theoretical Physics, Nauka, Moscow, 1972, p.119 (in Russian).

    Google Scholar 

  13. Lücke W., Acta Phys. Austriaca.55 (1984), 213.

    Google Scholar 

  14. Lücke W., J. Math. Phys.27 (1986), 1901.

    Google Scholar 

  15. Soloviev M.A., Sov. Phys.-Lebedev Inst. Rep.4 (1990), 45.

    Google Scholar 

  16. Efimov G.V.,Non-Local Interactions of Quantum Fields, Nauka, Moscow, 1977 (in Russian).

    Google Scholar 

  17. Efimov G.V.,Problems in Quantum Theory of Non-Local Interactions, Nauka, Moscow, 1985 (in Russian).

    Google Scholar 

  18. Efimov G.V., Quantum Field Theory and Quantum Statistics. Essays in Honour of the 60-th Birthday of E.S.Fradkin, Vol.1, Adam Hilger, Bristol, 1987, P. 545.

    Google Scholar 

  19. Soloviev M.A., Developments in Modern Mathematics, Chapman & Hall, London, 1992 (to appear).

    Google Scholar 

  20. Streater R.F., Wightman A.S., PCT, Spin and Statistics and All That (1964), W. A. Benjamin Inc. New York-Amsterdam.

    Google Scholar 

  21. Jaffe A., Phys. Rev.158 (1967), 1454.

    Google Scholar 

  22. Gelfand I.M., Shilov G.E.,Generalized Functions, Vol.2, Academic Press, New York, 1968.

    Google Scholar 

  23. Kawai T., J. Faculty of Sci. Univ. of Tokyo1A (1970), 465.

    Google Scholar 

  24. Soloviev M.A.,Convolution with Distributions Carried by Cones, Preprint ITEP-140 (1977 (in Russian)).

  25. Lücke W., Commun. Math. Phys.65 (1979), 77.

    Google Scholar 

  26. Soloviev M.A., Theor. Math. Phys.7 (1971), 183.

    Google Scholar 

  27. Constantinescu F., Taylor J.G., J. Math. Phys.15 (1974), 824.

    Google Scholar 

  28. Bümmerstede J., Lücke W., J. Math. Phys.16 (1975), 1203.

    Google Scholar 

  29. Hörmander L.,The Analysis of Linear Partial Differential Operators, Vol.1, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  30. Soloviev M.A., Theor. Math. Phys.15 (1973), 317.

    Google Scholar 

  31. Fubini S., Veneziano G., Nuovo Cim.A 64 (1969), 811.

    Google Scholar 

  32. Bordakci K., Mandelstam S., Phys. Rev.184 (1969), 1640.

    Google Scholar 

  33. Cohen A., Moore G., Nelson P., Polchinski J., Nucl. Phys.B 267 (1986), 143.

    Google Scholar 

  34. Green M.B., Schwartz J.H., Witten E.,Superstring Theory, Vol.1, Cambridge Univ. Press, Cambridge, 1987.

    Google Scholar 

  35. Polchinski J., Commun. Math. Phys.104 (1986), 37.

    Google Scholar 

  36. Soloviev M.A., Proc. Lebedev Phys. Inst.209 (1992), 121 (in Russian).

    Google Scholar 

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Authors
  1. V. Ya. Fainberg
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  2. M. A. Soloviev
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Additional information

In memory of Michael Polivanov, the remarkable personality and scientist

Department of Theoretical Physics, P. N. Lebedev Physical Institute. E-mail: theordep@sci.fian.msk.su. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 3, pp. 514–528, December, 1992.

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Fainberg, V.Y., Soloviev, M.A. Nonlocalizability and asymptotical commutativity. Theor Math Phys 93, 1438–1449 (1992). https://doi.org/10.1007/BF01016400

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  • DOI: https://doi.org/10.1007/BF01016400

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