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Vacuum Polarization in a Zero-Range Potential Field

  • Elementary Particles and Fields
  • Theory
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Abstract

The effects of vacuum polarization for a massless scalar field φ(x) in the vicinity of a pointlike source that has a zero-range potential are analyzed in four-dimensional Minkowski space. An exact expression for the regularized scalar-field Hadamard function is obtained by means of the technique of self-adjoint extensions, and the renormalized vacuum expectation values of the scalar field squared, ⟨φ2 (x)⟩ren, and of the operator of the scalar-field energy—momentum tensor, ⟨Tμν(x)⟩ren, are calculated.

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References

  1. R. de I. Kronig and W. G. Penney, Proc. R. Soc. London, Ser. A 130, 499 (1931).

    Article  ADS  Google Scholar 

  2. Yu. N. Demkov and V. N. Ostrovskii, Method of Zero-Range Potentials in Atomic Physics (Leningr. Gos. Univ., Leningrad, 1975) [in Russian]).

    Google Scholar 

  3. S. G. Mamaev and N. N. Trunov, Russ. Phys. J. 23, 551 (1980; Sov. J. Nucl. Phys. 35, 612 (1982).

    Google Scholar 

  4. M. Bordag, D. Henning, and D. Robaschik, J. Phys. A 25, 4483 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  5. J. M. Muños-Castañeda, J. Moteos Guilarte, and M. Mosquera, Phys. Rev. D 87, 105020 (2013).

    Article  Google Scholar 

  6. Yu.V. Grats, Phys. At. Nucl. 81, 253 (2018).

    Article  Google Scholar 

  7. Yu.V. Grats and P. Spirin, Eur. Phys. J. C 77, 101 (2017).

    Article  ADS  Google Scholar 

  8. M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis. Self-Adjointness (Academic, New York, London, 1975).

    MATH  Google Scholar 

  9. S. Albeverio, F. Gesztezy, R. Hoeg-Krohn, and H. Holden, Solvable Models in Quantum Mechanics (World Scientific, Singapore, 1995).

    Google Scholar 

  10. D. M. Gitman, I. V. Tyutin, and B. L. Voronov, Self-Adjoint Extensions in Quantum Mechanics (Springer, New York, 2012).

    Book  MATH  Google Scholar 

  11. R. W. Jackiw, Diverse Topics in Theoretical and Mathematical Physics, Advanced Series in Mathematical Physics (World Scientific, Singapore, 1995), Sect. 13).

    Book  MATH  Google Scholar 

  12. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge Univ. Press, Cambridge, 1982).

    Book  MATH  Google Scholar 

  13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Nauka, Moscow, 1971; Academic, New York, 1980).

    MATH  Google Scholar 

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Acknowledgements

I am grateful to A.V. Borisov for a discussion on the results obtained in the present study and for enlightening comments.

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Authors and Affiliations

  1. Faculty of Physics, Moscow State University, Moscow, 119991, Russia

    Yu. V. Grats

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  1. Yu. V. Grats
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Correspondence to Yu. V. Grats.

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Grats, Y.V. Vacuum Polarization in a Zero-Range Potential Field. Phys. Atom. Nuclei 82, 153–157 (2019). https://doi.org/10.1134/S106377881902008X

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  • DOI: https://doi.org/10.1134/S106377881902008X

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