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TMF, 2015, Volume 183, Number 2, Pages 163–176 (Mi tmf8868)  

This article is cited in 6 scientific papers (total in 6 papers)

New approach to the quantization of the Yang–Mills field

A. A. Slavnovab

a Steklov Mathematical Institute of RAS, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia

Abstract: We review papers on a new method for quantizing the Yang–Mills field applicable both in perturbation theory and beyond it. We show that in the modified formulation of the Yang–Mills theory leading to a formal perturbation theory that coincides with the standard one, there exist soliton solutions of the classical equations of motion.

Keywords: non-Abelian gauge invariance, quantization, quantization nonuniqueness, soliton

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was done at the Steklov Mathematical Institute of RAS and supported by the Russian Science Foundation (Grant No. 14-05-00005).


DOI: https://doi.org/10.4213/tmf8868

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English version:
Theoretical and Mathematical Physics, 2015, 183:2, 585–596

Bibliographic databases:

Document Type: Article
Received: 10.02.2015

Citation: A. A. Slavnov, “New approach to the quantization of the Yang–Mills field”, TMF, 183:2 (2015), 163–176; Theoret. and Math. Phys., 183:2 (2015), 585–596

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    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. A. Slavnov, “Nonperturbative quantization of models of massive non-Abelian gauge fields with spontaneously broken symmetry”, Theoret. and Math. Phys., 189:2 (2016), 1645–1650  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Zharinov, “Bäcklund transformations”, Theoret. and Math. Phys., 189:3 (2016), 1681–1692  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. D. V. Bykov, “Cyclic gradings of Lie algebras and Lax pairs for $\sigma$-models”, Theoret. and Math. Phys., 189:3 (2016), 1734–1741  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Moshin P.Yu. Reshetnyak A.A., “Finite field-dependent BRST-anti-BRST transformations: Jacobians and application to the Standard Model”, Int. J. Mod. Phys. A, 31:20-21 (2016), 1650111  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. A. Slavnov, “A possibility to describe models of massive non-Abelian gauge fields in the framework of a renormalizable theory”, Theoret. and Math. Phys., 193:3 (2017), 1826–1833  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. A. A. Slavnov, “Renormalizability and unitarity of the Englert–Broute–Higgs–Kibble model”, Theoret. and Math. Phys., 197:2 (2018), 1611–1614  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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