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TMF, 1972, Volume 12, Number 3, Pages 305–330 (Mi tmf2994)  

This article is cited in 38 scientific papers (total in 41 papers)

On scaling asymptotics in quantum field theory. II

N. N. Bogolyubov, V. S. Vladimirov, A. N. Tavkhelidze


Abstract: The probability of deep inelastic scattering of electrons by protons is expressed in terms of the imaginary part of the amplitude for the virtual Compton effect. Causality of the form factors $W_1$ and $W_2$ is established. The Jest–Lehmann–Dy son representation is used for causal form factors; restrictions on the weight functions of this representation lead to scaling asymptotics of the deep inelastic amplitude. Under these conditions the current commutator's behavior near the light cone is found and the asymptotic behavior of the form factors is related to the singularities on the light cone.

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English version:
Theoretical and Mathematical Physics, 1972, 12:3, 839–858

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Document Type: Article
Received: 29.05.1972

Citation: N. N. Bogolyubov, V. S. Vladimirov, A. N. Tavkhelidze, “On scaling asymptotics in quantum field theory. II”, TMF, 12:3 (1972), 305–330; Theoret. and Math. Phys., 12:3 (1972), 839–858

Citation in format AMSBIB
\Bibitem{BogVlaTav72}
\by N.~N.~Bogolyubov, V.~S.~Vladimirov, A.~N.~Tavkhelidze
\paper On scaling asymptotics in quantum field theory.~II
\jour TMF
\yr 1972
\vol 12
\issue 3
\pages 305--330
\mathnet{http://mi.mathnet.ru/tmf2994}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=475413}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 12
\issue 3
\pages 839--858
\crossref{https://doi.org/10.1007/BF01035603}


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    This publication is cited in the following articles:
    1. B. I. Zavialov, “Aling of electromagnetic form factors and the behavior of their Fourier transforms in the neighborhood of the light cone”, Theoret. and Math. Phys., 17:2 (1973), 1074–1081  mathnet  crossref  mathscinet  zmath
    2. N. I. Usyukina, “Current commutators on the light cone and perturbation theory”, Theoret. and Math. Phys., 17:3 (1973), 1200–1209  mathnet  crossref  zmath
    3. B. M. Barbashov, V. V. Nesterenko, “Eikonal approximation for deep inelastic scattering in scalar electrodynamics”, Theoret. and Math. Phys., 16:1 (1973), 665–671  mathnet  crossref
    4. B. I. Zavialov, “On the behavior of the electromagnetic form factors in the neighborhood of the light cone”, Theoret. and Math. Phys., 16:1 (1973), 672–675  mathnet  crossref
    5. È. Wieczorek, V. A. Matveev, D. Robaschik, “Scaling behavior of the amplitude of virtual comption scattering in the framework of the Dyson–Jost–Lehmann representation”, Theoret. and Math. Phys., 19:1 (1974), 315–324  mathnet  crossref
    6. B. I. Zavialov, ““Quasiasymptotics” of generalized functions and scaling of electromagnetic form factors”, Theoret. and Math. Phys., 19:2 (1974), 426–432  mathnet  crossref  mathscinet  zmath
    7. È. Wieczorek, B. Derfel', N. V. Krasnikov, V. A. Matveev, D. Robaschik, K. G. Chetyrkin, “Scaling behavior of deep inelastic scattering on massless target particles”, Theoret. and Math. Phys., 20:3 (1974), 841–845  mathnet  crossref  mathscinet
    8. A. M. Kotsinyan, “Investigation of the azimuthal dependence of inclusive electroproduction by the method of operator expansions on the light cone”, Theoret. and Math. Phys., 24:2 (1975), 776–779  mathnet  crossref
    9. È. Wieczorek, V. A. Matveev, D. Robaschik, A. N. Tavkhelidze, “Scaling solutions for matrix elements of currents in conformally invariant theories”, Theoret. and Math. Phys., 22:1 (1975), 1–12  mathnet  crossref  mathscinet
    10. È. Wieczorek, B. Gaier, T. Gernits, V. A. Matveev, D. Robaschik, A. N. Tavkhelidze, “Scaling for the fixed-angle scattering amplitude in the framework of the Dyson–Jost–Lehmann representation”, Theoret. and Math. Phys., 28:2 (1976), 699–708  mathnet  crossref  mathscinet
    11. B. A. Magradze, V. A. Matveev, “Self-similar solutions in a conformally invariant theory with continuous mass spectrum”, Theoret. and Math. Phys., 31:3 (1977), 476–478  mathnet  crossref
    12. B. I. Zavialov, “Bjorken asymptotic behavior of deep inelastic scattering form factors and the general principles of field theory”, Theoret. and Math. Phys., 33:3 (1977), 1040–1046  mathnet  crossref  mathscinet
    13. A. V. Kudinov, K. G. Chetyrkin, “Scaling at short distances and the behavior of $R(s)$ as $s\to\infty$”, Theoret. and Math. Phys., 34:1 (1978), 86–89  mathnet  crossref
    14. A. V. Kiselev, V. A. Petrov, A. Yu. Taranov, “Inclusive electroproduction of hadrons in the fragmentation region of the virtual photon”, Theoret. and Math. Phys., 34:3 (1978), 198–202  mathnet  crossref
    15. V. A. Smirnov, “Connection between the asymptotic behavior of electromagnetic form factors and the singularities of their Fourier transforms”, Theoret. and Math. Phys., 35:2 (1978), 455–458  mathnet  crossref
    16. S. I. Maximov, “Scaling of inclusive form factors with respect to a generalized scaled variable”, Theoret. and Math. Phys., 38:3 (1979), 212–219  mathnet  crossref  mathscinet
    17. A. V. Kiselev, M. A. Mestvirishvili, V. E. Rochev, “Breaking of scale invariance and behavior of the spectral function in the Jost–Lehmann–Dyson representation”, Theoret. and Math. Phys., 39:1 (1979), 305–313  mathnet  crossref
    18. G. Sh. Dzhaparidze, V. A. Petrov, “Deser–Gilbert–Sudarshan representation for fungtions with an isolated branch in the spectrum”, Theoret. and Math. Phys., 40:1 (1979), 649–651  mathnet  crossref  mathscinet  isi
    19. V. S. Vladimirov, B. I. Zavialov, “Tauberian theorems in quantum field theory”, Theoret. and Math. Phys., 40:2 (1979), 660–677  mathnet  crossref  mathscinet  isi
    20. V. A. Matveev, R. M. Muradyan, A. N. Tavkhelidze, “A method of quark counting for inclusive processes”, Theoret. and Math. Phys., 40:3 (1979), 778–785  mathnet  crossref  mathscinet  isi
    21. A. N. Kvinikhidze, B. A. Magradze, V. A. Matveev, M. A. Mestvirishvili, A. N. Tavkhelidze, “Integral equation for the causal distributions and their self-similar asymptotic behavior in the ladder $\Phi^3$ model”, Theoret. and Math. Phys., 45:3 (1980), 1041–1048  mathnet  crossref  mathscinet  isi
    22. A. V. Efremov, A. V. Radyushkin, “Field theory approach to processes with large momentum transfer. I. Deep inelastic scattering”, Theoret. and Math. Phys., 44:1 (1980), 573–584  mathnet  crossref  mathscinet  isi
    23. V. R. Garsevanishvili, Ya. Z. Darbaidze, Z. R. Menteshashvili, “Deep inelastic scattering of leptons on nuclei”, Theoret. and Math. Phys., 42:1 (1980), 32–37  mathnet  crossref  isi
    24. B. I. Zavialov, “Jost–Lehmann–Dyson representation in the spaces $S'_\alpha$”, Theoret. and Math. Phys., 49:2 (1981), 945–951  mathnet  crossref  mathscinet  isi
    25. F. A. Lunev, “Invariant current algebra on the light cone and deep inelastic lepton-hadron scattering. I”, Theoret. and Math. Phys., 52:2 (1982), 772–776  mathnet  crossref  isi
    26. V. S. Vladimirov, B. I. Zavialov, “Self-similar asymptotic behavior of causal functions and their behavior on the light cone”, Theoret. and Math. Phys., 50:2 (1982), 105–126  mathnet  crossref  mathscinet  isi
    27. A. D. Linkevich, V. I. Savrin, N. B. Skachkov, “Structure functions of relativistic systems composed of two spin 1/2 particles”, Theoret. and Math. Phys., 53:1 (1982), 955–962  mathnet  crossref  mathscinet  isi
    28. N. N. Bogolyubov, A. A. Logunov, G. I. Marchuk, “Vasilii Sergeevich Vladimirov (on his sixtieth birthday)”, Russian Math. Surveys, 38:1 (1983), 231–243  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. F. A. Lunev, “Invariant current algebra on the light cone and deep inelastic lepton-hadron scattering. II”, Theoret. and Math. Phys., 55:3 (1983), 569–580  mathnet  crossref  mathscinet  isi
    30. I. L. Solovtsov, D. V. Shirkov, “The analytic approach in quantum chromodynamics”, Theoret. and Math. Phys., 120:3 (1999), 1220–1244  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. V. S. Vladimirov, “Nikolai Nikolaevich Bogolyubov and Mathematics”, Proc. Steklov Inst. Math., 228 (2000), 1–10  mathnet  mathscinet  zmath
    32. Yu. N. Drozhzhinov, B. I. Zavialov, “Wiener-Type Tauberian Theorems for Generalized Functions on the Half-Axis”, Proc. Steklov Inst. Math., 228 (2000), 43–51  mathnet  mathscinet  zmath
    33. Magradze, BA, “An analytic approach to perturbative QCD”, International Journal of Modern Physics A, 15:17 (2000), 2715  crossref  isi
    34. V. S. Vladimirov, “N. N. Bogolyubov and Mathematics”, Russian Math. Surveys, 56:3 (2001), 607–613  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    35. Nesterenko, AV, “Massive analytic invariant charge in QCD”, Physical Review D, 71:1 (2005), 016009  crossref  isi
    36. 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
    37. Yu. N. Drozhzhinov, B. I. Zavialov, “Applications of Tauberian theorems in some problems in mathematical physics”, Theoret. and Math. Phys., 157:3 (2008), 1678–1693  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    38. Aref'eva, IY, “TIME MACHINE AT THE LHC”, International Journal of Geometric Methods in Modern Physics, 5:4 (2008), 641  crossref  mathscinet  isi
    39. O. P. Solovtsova, V. I. Lashkevich, “The Jost–Lehmann–Dyson representation and target mass effects”, Theoret. and Math. Phys., 160:3 (2009), 1260–1273  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    40. V. S. Vladimirov, “Scale-invariant asymptotic (automodel) behavior in quantum field theory”, Theoret. and Math. Phys., 170:1 (2012), 97–99  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    41. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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