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TMF, 1982, Volume 50, Number 2, Pages 195–206 (Mi tmf2102)  

This article is cited in 27 scientific papers (total in 27 papers)

$1/n$ expansion: clculation of the exponent $\eta$ in the order $1/n^3$ by the conformal bootstrap method

A. N. Vasil'ev, Yu. M. Pis'mak, Yu. R. Khonkonen

Leningrad State University

Abstract: For arbitrary causal functions satisfying the spectral condition Tauberian theorems are established which give a correspondence between their self-similar asymptotic behavior and their asymptotic behavior in the neighborhood of the light cone.

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English version:
Theoretical and Mathematical Physics, 1982, 50:2, 127–134

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Received: 23.01.1981

Citation: A. N. Vasil'ev, Yu. M. Pis'mak, Yu. R. Khonkonen, “$1/n$ expansion: clculation of the exponent $\eta$ in the order $1/n^3$ by the conformal bootstrap method”, TMF, 50:2 (1982), 195–206; Theoret. and Math. Phys., 50:2 (1982), 127–134

Citation in format AMSBIB
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\by A.~N.~Vasil'ev, Yu.~M.~Pis'mak, Yu.~R.~Khonkonen
\paper $1/n$ expansion: clculation of the exponent $\eta$ in the order $1/n^3$ by the conformal bootstrap method
\jour TMF
\yr 1982
\vol 50
\issue 2
\pages 195--206
\mathnet{http://mi.mathnet.ru/tmf2102}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 50
\issue 2
\pages 127--134
\crossref{https://doi.org/10.1007/BF01015292}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PH72200002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Vasil'ev, M. Yu. Nalimov, “Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space”, Theoret. and Math. Phys., 55:2 (1983), 423–431  mathnet  crossref  isi
    2. A. N. Vasil'ev, M. M. Perekalin, Yu. M. Pis'mak, “On the possibility of conformal infrared asymptotic behavior in non-Abelian Yang–Mills theory”, Theoret. and Math. Phys., 55:3 (1983), 529–536  mathnet  crossref  isi
    3. A. N. Vasil'ev, M. Yu. Nalimov, “The $CP^{N-1}$ model: Calculation of anomalous dimensions and the mixing matrices in the order $1/N$”, Theoret. and Math. Phys., 56:1 (1983), 643–653  mathnet  crossref  isi
    4. A. N. Vasil'ev, M. M. Perekalin, Yu. M. Pis'mak, “Conformal bootstrap equations for Yang–Mills type interaction”, Theoret. and Math. Phys., 60:2 (1984), 846–847  mathnet  crossref  isi
    5. L. Ts. Adzhemyan, A. N. Vasil'ev, Yu. M. Pis'mak, “Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. II. Infrared representation and large-distance behavior”, Theoret. and Math. Phys., 68:3 (1986), 855–865  mathnet  crossref  isi
    6. A. N. Vasil'ev, S. È. Derkachev, N. A. Kivel', A. S. Stepanenko, “Proof of conformal invariance in the critical regime for models of Gross–Neveu type”, Theoret. and Math. Phys., 92:3 (1992), 1047–1054  mathnet  crossref  mathscinet  isi
    7. A. N. Vasil'ev, S. È. Derkachev, N. A. Kivel', A. S. Stepanenko, “The $1/n$ expansion in the Gross–Neveu model: Conformal bootstrap calculation of the index $\eta$ in order $1/n^3$”, Theoret. and Math. Phys., 94:2 (1993), 127–136  mathnet  crossref  isi
    8. A. N. Vasil'ev, A. S. Stepanenko, “A method of calculating the critical dimensions of composite operators in the massless nonlinear $\sigma$ model”, Theoret. and Math. Phys., 95:1 (1993), 471–481  mathnet  crossref  zmath
    9. A. N. Vasil'ev, A. S. Stepanenko, “The $1/n$ expansion in the Gross–Neveu model: Conformal bootstrap calculation of the exponent $1/\nu$ to the order $1/n^2$”, Theoret. and Math. Phys., 97:3 (1993), 1349–1354  mathnet  crossref  mathscinet  isi
    10. S. È. Derkachev, A. N. Manashov, “Critical dimensions of composite operators in the nonlinear $\sigma$-model”, Theoret. and Math. Phys., 116:3 (1998), 1034–1049  mathnet  crossref  crossref  mathscinet  isi
    11. Ciuchini, M, “Computation of quark mass anomalous dimension at O(1/N-f(2)) in quantum chromodynamics”, Nuclear Physics B, 579:1–2 (2000), 56  crossref  isi
    12. N. V. Antonov, A. S. Kapustin, A. V. Malyshev, “Effects of turbulent transfer on critical behavior”, Theoret. and Math. Phys., 169:1 (2011), 1470–1480  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    13. M. V. Polyakov, A. A. Vladimirov, “Leading infrared logarithms for the $\sigma$-model with fields on an arbitrary Riemann manifold”, Theoret. and Math. Phys., 169:1 (2011), 1499–1506  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    14. A. L. Pismenskii, “Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method”, Theoret. and Math. Phys., 185:1 (2015), 1516–1521  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    15. Pismensky A.L., “Calculation of Critical Index Eta of the Phi(3)-Theory in Four-Loop Approximation By the Conformal Bootstrap Technique”, Int. J. Mod. Phys. A, 30:24 (2015), 1550138  crossref  isi
    16. Pismensky A.L. Pis'mak Yu.M., “Scaling Violation in Massless Scalar Quantum Field Models in Logarithmic Dimensions”, J. Phys. A-Math. Theor., 48:32, SI (2015), 325401  crossref  isi
    17. Gracey J.A. Luthe T. Schroder Y., “Four loop renormalization of the Gross-Neveu model”, Phys. Rev. D, 94:12 (2016), 125028  crossref  mathscinet  isi
    18. Bagaev A.A. Pis'mak Yu.M., “The 0D Quantum Field Theory: Multiple Integrals Via Background Field Formalism”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), ed. Motygin O. Kiselev A. Kapitanova P. Goray L. Kazakov A. Kirpichnikova A., IEEE, 2016, 41–45  isi
    19. Manashov A.N. Skvortsov E.D., “Higher-spin currents in the Gross-Neveu model at 1/n2”, J. High Energy Phys., 2017, no. 1, 132  crossref  mathscinet  isi  scopus
    20. Skvortsov E.D., “On (Un)Broken Higher-Spin Symmetry in Vector Models”, Higher Spin Gauge Theories, ed. Brink L. Henneaux M. Vasiliev M., World Scientific Publ Co Pte Ltd, 2017, 103–137  isi
    21. Nesterenko A., “Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach”, Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach, Elsevier Science BV, 2017, 1–204  isi
    22. Kompaniets M.V. Panzer E., “Minimally Subtracted Six-Loop Renormalization of O(N)-Symmetric Phi(4) Theory and Critical Exponents”, Phys. Rev. D, 96:3 (2017), 036016  crossref  isi
    23. Manashov A.N. Skvortsov E.D. Strohmaier M., “Higher Spin Currents in the Critical O(N) Vector Model At 1/N-2”, J. High Energy Phys., 2017, no. 8, 106  crossref  isi
    24. Manashov A.N. Strohmaier M., “Correction Exponents in the Gross-Neveu-Yukawa Model At 1/N-2”, Eur. Phys. J. C, 78:6 (2018), 454  crossref  isi
    25. Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032  crossref  mathscinet  zmath  isi  scopus
    26. Pismensky A.L., “Application of Eta-Expansion Technique to the Phi(3)-Theory in Arbitrary Dimension”, Int. J. Mod. Phys. A, 33:35 (2018), 1850209  crossref  mathscinet  zmath  isi  scopus
    27. Kotikov A.V. Teber S., “Multi-Loop Techniques For Massless Feynman Diagram Calculations”, Phys. Part. Nuclei, 50:1 (2019), 1–41  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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