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TMF, 2003, Volume 136, Number 1, Pages 3–19 (Mi tmf217)  

This article is cited in 15 scientific papers (total in 15 papers)

Fourier Transformation of the Renormalization-Invariant Coupling

D. V. Shirkov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: We discuss integral transformations of the QCD renormalization-invariant coupling (“running coupling constant”). Special attention is paid to the Fourier transformation, i.e., to the transition from the space-time to the energy-momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation.

Keywords: Tauberian theorem, IR behavior in QCD, Fourier transformation

DOI: https://doi.org/10.4213/tmf217

Full text: PDF file (348 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 136:1, 893–907

Bibliographic databases:

Received: 02.12.2002

Citation: D. V. Shirkov, “Fourier Transformation of the Renormalization-Invariant Coupling”, TMF, 136:1 (2003), 3–19; Theoret. and Math. Phys., 136:1 (2003), 893–907

Citation in format AMSBIB
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\paper Fourier Transformation of the Renormalization-Invariant Coupling
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\jour Theoret. and Math. Phys.
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\issue 1
\pages 893--907
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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. Furui S, Nakajima H, “Infrared features of the Landau gauge QCD”, Physical Review D, 69:7 (2004), 074505  crossref  adsnasa  isi  scopus  scopus
    2. A. I. Alekseev, “Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large $Q^2$”, Theoret. and Math. Phys., 145:2 (2005), 1559–1575  mathnet  crossref  crossref  adsnasa  isi  elib
    3. Alekseev AI, “Synthetic running coupling of QCD”, Few-Body Systems, 40:1–2 (2006), 57–70  crossref  adsnasa  isi  scopus  scopus
    4. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387  crossref  adsnasa  isi  scopus  scopus
    5. Shirkov, D, “Nonpower expansions for QCD observables at low energies”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 51  crossref  adsnasa  isi  elib  scopus  scopus
    6. D. V. Shirkov, I. L. Solovtsov, “Ten years of the analytic perturbation theory in QCD”, Theoret. and Math. Phys., 150:1 (2007), 132–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Baldicchi, M, “Bound-state approach to the QCD coupling constant at low-energy scales”, Physical Review Letters, 99:24 (2007), 242001  crossref  adsnasa  isi  elib  scopus  scopus
    8. Baldicchi M, Nesterenko AV, Prosperi GM, et al, “QCD coupling below 1 GeV from the quarkonium spectrum”, Physical Review D, 77:3 (2008), 034013  crossref  adsnasa  isi  elib  scopus  scopus
    9. Cvetic, G, “Analytic QCD - a Short Review”, Brazilian Journal of Physics, 38:3B (2008), 371  adsnasa  isi
    10. Ganbold G., “QCD running coupling in low-energy region”, Phys Rev D, 81:9 (2010), 094008  crossref  adsnasa  isi  elib  scopus  scopus
    11. Ganbold G., “Hadron Spectrum and the Infrared Behavior of QCD Coupling”, 19th International Spin Physics Symposium, Journal of Physics Conference Series, 295, no. 1, 2011  isi
    12. Simonov Yu.A., “Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism”, Phys Atomic Nuclei, 74:8 (2011), 1223–1229  crossref  adsnasa  isi  elib  scopus  scopus
    13. Ganbold G., “Hadron Spectrum and Infrared-Finite Behavior of QCD Running Coupling”, Phys. Part. Nuclei, 43:1 (2012), 79–105  crossref  isi  elib  scopus  scopus
    14. Ganbold G., “Quark-Antiquark Bound States and QCD Running Coupling Within Infrared Confinement”, Phys. Part. Nuclei, 45:1 (2014), 10–12  crossref  adsnasa  isi  scopus  scopus
    15. Blaschke D., Dubinin A., Turko L., “Mott-Hadron Resonance Gas and Lattice QCD Thermodynamics”, Phys. Part. Nuclei, 46:5 (2015), 732–736  crossref  mathscinet  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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