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Anomalous dimensions of composite operators in scalar field theories

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The problem of calculation of one-loop anomalous dimensions of composite operators can be reformulated as a spectral problem for the Hamiltonian of an N-particle quantum-mechanical system with pairwise interaction. We give a brief review of the corresponding technique using as examples the scalar field theories φ3 and φ4.As an application we calculate the exact anomalous dimensions for operators of a certain type. Bibliography: 27 titles.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia

    S. E. Derkahov

  2. St. Petersburg State University, St. Petersburg, Russia

    A. N. Manashov

Authors
  1. S. E. Derkahov
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  2. A. N. Manashov
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Correspondence to S. E. Derkahov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 374, 2010, pp. 136–169.

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Derkahov, S.E., Manashov, A.N. Anomalous dimensions of composite operators in scalar field theories. J Math Sci 168, 837–855 (2010). https://doi.org/10.1007/s10958-010-0032-9

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  • DOI: https://doi.org/10.1007/s10958-010-0032-9

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