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Mixed Type Regularizations and Nonlogarithmic Singularities

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In this paper we discuss dimensional and cutoff regularizations, using the heat kernel method as an example. The regularization modifications by adding to a Green function a special type operator are considered. In particular, we show that the dimensional regularization can lead to nonlogarithmic divergences.

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References

  1. J. C. Collins, Renormalization: an Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion, Cambridge University Press, Cambridge (1984).

    Book  Google Scholar 

  2. G. ’t Hooft and M. Veltman, “Regularization and renormalization of gauge fields,” Nucl. Phys. B, 44, 189–213 (1972).

  3. C. G. Bollini and J. J. Giambiaggi, “Lowest order ivergent graphs in v-dimensional space,” Phys. Lett. B, 40, 566–568 (1972).

    Article  Google Scholar 

  4. J. Polchinski, “Renormalization and effective lagrangians,” Nuclear Physics B, 231(2), 269–295 (1984).

    Article  Google Scholar 

  5. A. V. Ivanov and N. V. Kharuk, “Quantum equation of motion and two-loop cutoff renormalization for 𝜙3 model,” Zap. Nauchn. Semin. POMI, 487, 151–166 (2019).

    Google Scholar 

  6. R. P. Feynman, “Space-time approach to quantum electrodynamics,” Phys. Review, 76, 769 (1949).

    Article  MathSciNet  Google Scholar 

  7. B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York (1965).

    MATH  Google Scholar 

  8. P. B. Gilkey, “The spectral geometry of a Riemannian manifold,” J. Diff. Geom., 10, 601–618 (1975).

    MathSciNet  MATH  Google Scholar 

  9. A. V. Ivanov and N. V. Kharuk, “Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line,” TMF, 205, No. 2, 242–261 (2020).

    Article  Google Scholar 

  10. M. Lüscher, “Dimensional regularisation in the presence of large background fields,” Annal. Phys., 142, 359–392 (1982).

  11. A. V. Ivanov and N. V. Kharuk, “Two-loop cutoff renormalization of 4-D Yang–Mills effective action,” J. Phys. G: Nucl. Part. Phys., 48 015002, (2020).

  12. L. D. Faddeev and A. A. Slavnov, Gauge Fields: an Introduction to Quantum Theory, Frontiers in Physics, Addison-Wesley 83 (1991).

  13. K. Hagiwara, S. Ishihara, R. Szalapski, and D. Zeppenfeld, “Low energy effects of new interactions in the electroweak boson sector,” Phys. Rev. D, 48(5), 2182–2203 (1993).

    Article  Google Scholar 

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Authors and Affiliations

  1. St.Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Leonhard Euler International Mathematical Institute; ITMO University, St.Petersburg, Russia

    N. V. Kharuk

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  1. N. V. Kharuk
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Correspondence to N. V. Kharuk.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 494, 2020, pp. 242–249.

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Kharuk, N.V. Mixed Type Regularizations and Nonlogarithmic Singularities. J Math Sci 264, 362–367 (2022). https://doi.org/10.1007/s10958-022-06003-7

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  • DOI: https://doi.org/10.1007/s10958-022-06003-7

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