RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 1981, Volume 47, Number 3, Pages 291–306 (Mi tmf2383)  

This article is cited in 44 scientific papers (total in 44 papers)

$1/n$ Expansion: Calculation of the exponents $\eta$ and $\nu$ in the order $1/n^2$ for arbitrary number of dimensions

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

Leningrad State University

Abstract: A scheme proposed earlier [1] is used to calculate the critical exponents $\eta$ and $\nu$ in the order $1/n^2$ for arbitrary number of dimensions of space. Some technical aspects of the calculation of massless diagrams are of independent interest.

Full text: PDF file (2288 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1981, 47:3, 465–475

Bibliographic databases:

Received: 21.01.1980

Citation: A. N. Vasil'ev, Yu. M. Pis'mak, Yu. R. Khonkonen, “$1/n$ Expansion: Calculation of the exponents $\eta$ and $\nu$ in the order $1/n^2$ for arbitrary number of dimensions”, TMF, 47:3 (1981), 291–306; Theoret. and Math. Phys., 47:3 (1981), 465–475

Citation in format AMSBIB
\Bibitem{VasPisKho81}
\by A.~N.~Vasil'ev, Yu.~M.~Pis'mak, Yu.~R.~Khonkonen
\paper $1/n$~Expansion: Calculation of the exponents~$\eta$ and~$\nu$ in the order~$1/n^2$ for arbitrary number of dimensions
\jour TMF
\yr 1981
\vol 47
\issue 3
\pages 291--306
\mathnet{http://mi.mathnet.ru/tmf2383}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 47
\issue 3
\pages 465--475
\crossref{https://doi.org/10.1007/BF01019296}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MX63700001}


Linking options:
  • http://mi.mathnet.ru/eng/tmf2383
  • http://mi.mathnet.ru/eng/tmf/v47/i3/p291

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Vasil'ev, Yu. M. Pis'mak, Yu. R. Khonkonen, “Infrared asymptotic behavior of the gluon propagator”, Theoret. and Math. Phys., 48:3 (1981), 750–758  mathnet  crossref  isi
    2. 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”, Theoret. and Math. Phys., 50:2 (1982), 127–134  mathnet  crossref  isi
    3. 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
    4. 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
    5. N. I. Usyukina, “Calculation of many-loop diagrams of perturbation theory”, Theoret. and Math. Phys., 54:1 (1983), 78–81  mathnet  crossref  isi
    6. D. I. Kazakov, “Calculation of Feynman diagrams by the “Uniqueness” method”, Theoret. and Math. Phys., 58:3 (1984), 223–230  mathnet  crossref  mathscinet  isi
    7. D. I. Kazakov, “Many-loop calculations: The uniqueness method and functional equations”, Theoret. and Math. Phys., 62:1 (1985), 84–89  mathnet  crossref  isi
    8. S. G. Gorishnii, A. P. Isaev, “An approach to the calculation of many-loop massless Feynman integrals”, Theoret. and Math. Phys., 62:3 (1985), 232–240  mathnet  crossref  mathscinet  isi
    9. D. I. Kazakov, A. V. Kotikov, “Uniqueness method: Multiloop calculations in QCD”, Theoret. and Math. Phys., 73:3 (1987), 1264–1274  mathnet  crossref  isi
    10. A. V. Kotikov, “Method of calculating the moments of the structure functions of deep inelastic scattering in quantum chromodynamics”, Theoret. and Math. Phys., 78:2 (1989), 134–143  mathnet  crossref  mathscinet  isi
    11. N. I. Usyukina, “Algorithm for calculating massless Feynman diagrams”, Theoret. and Math. Phys., 79:1 (1989), 385–391  mathnet  crossref  mathscinet  isi
    12. N. I. Usyukina, “Calculation of multiloop diagrams of arbitrary orders”, Theoret. and Math. Phys., 87:3 (1991), 627–632  mathnet  crossref  isi
    13. N. I. Usyukina, “Calculation in five loops of a multiloop diagram of special form”, Theoret. and Math. Phys., 88:1 (1991), 683–685  mathnet  crossref  isi
    14. 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
    15. 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
    16. 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
    17. 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
    18. Ciuchini, M, “Quark mass anomalous dimension at O(1/N-f(2)) in QCD”, Physics Letters B, 458:1 (1999), 117  crossref  isi
    19. Ali, DB, “Four loop wave function renormalization in the non-abelian Thirring model”, Nuclear Physics B, 605:1–3 (2001), 337  crossref  isi
    20. Smirnov, VA, “Applied asymptotic expansions in momenta and masses - Introduction”, Applied Asymptotic Expansions in Momenta and Masses, 177 (2002), 1  crossref  isi
    21. 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
    22. A. V. Kotikov, “The property of maximal transcendentality: Calculation of master integrals”, Theoret. and Math. Phys., 176:1 (2013), 913–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. I. Gonzalez, I. Kondrashuk, “Box ladders in a noninteger dimension”, Theoret. and Math. Phys., 177:2 (2013), 1515–1539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. 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
    25. K. S. Karpov, Yu. M. Pis'mak, “Algebraic calculation of the resolvent of a generalized quantum oscillator in a space of dimension $D$”, Theoret. and Math. Phys., 185:1 (2015), 1454–1461  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. 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
    27. 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
    28. 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
    29. 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
    30. A. V. Kotikov, “The property of maximal transcendentality: Calculation of Feynman integrals”, Theoret. and Math. Phys., 190:3 (2017), 391–401  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. S. Teber, A. V. Kotikov, “The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations”, Theoret. and Math. Phys., 190:3 (2017), 446–457  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. 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
    33. Hikida Ya. Wada T., “Anomalous dimensions of higher spin currents in large N CFTs”, J. High Energy Phys., 2017, no. 1, 032  crossref  mathscinet  isi  scopus
    34. Gubser S.S. Jepsen Ch. Parikh S. Trundy B., “O(N) and O(N) and O(N)”, J. High Energy Phys., 2017, no. 11, 107  crossref  isi
    35. 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
    36. 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
    37. 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
    38. A. V. Kotikov, S. Teber, “New results for a two-loop massless propagator-type Feynman diagram”, Theoret. and Math. Phys., 194:2 (2018), 284–294  mathnet  crossref  crossref  adsnasa  isi  elib
    39. 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
    40. Gonzalez I. Kondrashuk I. Notte-Cuello E.A. Parra-Ferrada I., “Multi-Fold Contour Integrals of Certain Ratios of Euler Gamma Functions From Feynman Diagrams: Orthogonality of Triangles”, Anal. Math. Phys., 8:4 (2018), 589–602  crossref  mathscinet  zmath  isi  scopus
    41. Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032  crossref  mathscinet  zmath  isi  scopus
    42. 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
    43. Kotikov A.V. Teber S., “Multi-Loop Techniques For Massless Feynman Diagram Calculations”, Phys. Part. Nuclei, 50:1 (2019), 1–41  crossref  isi
    44. S. Teber, A. V. Kotikov, “Review of electron–electron interaction effects in planar Dirac liquids”, Theoret. and Math. Phys., 200:2 (2019), 1222–1236  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:391
    Full text:160
    References:31
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020