Abstract:
We consider the theory of a massless scalar field ϕ with the gϕ3 coupling in a six-dimensional space. We use Bogoliubov's method of quasiaverages to study the possibility of a breaking of the original scaling symmetry and of the corresponding spontaneous generation of the effective Gϕ4 coupling. We show that the linearized compensation equation for the form factor of this coupling has a nontrivial solution through the third-order approximation. In the same approximation, the Bethe–Salpeter equation for a massless scalar bound state of two fields ϕ also has a solution. Matching the values of the form factor and the scalar field mass m at zero leads to a unique solution that gives a relation between the parameters of thegϕ3 coupling and the parameters G and m. We argue in favor of the stability of the nontrivial solution obtained.
Keywords:
effective coupling, quantum field theory, Bogoliubov's method of quasiaverages, compensation equation, nontrivial solution.
Citation:
B. A. Arbuzov, “Spontaneous Generation of Effective Interaction in a Renormalizable Quantum Field Theory Model”, TMF, 140:3 (2004), 367–387; Theoret. and Math. Phys., 140:3 (2004), 1205–1221
\Bibitem{Arb04}
\by B.~A.~Arbuzov
\paper Spontaneous Generation of Effective Interaction in a~Renormalizable Quantum Field Theory Model
\jour TMF
\yr 2004
\vol 140
\issue 3
\pages 367--387
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\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 140
\issue 3
\pages 1205--1221
\crossref{https://doi.org/10.1023/B:TAMP.0000039827.32271.1d}
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Linking options:
https://www.mathnet.ru/eng/tmf99
https://doi.org/10.4213/tmf99
https://www.mathnet.ru/eng/tmf/v140/i3/p367
This publication is cited in the following 26 articles:
B. A. Arbuzov, I. V. Zaitsev, “Nonperturbative Solutions in the Standard Model Theories”, Phys. Part. Nuclei, 55:2 (2024), 189
Arbuzov B.A., Zaitsev V I., “Calculation of the Contribution to Muon G-2 Due to the Effective Anomalous Three Boson Interaction and the New Experimental Result”, Int. J. Mod. Phys. A, 36:29 (2021), 2150223
Arbuzov B.A. Zaitsev I.V., “Looking For Nonperturbative Effects of the Electroweak Interaction At the Lhc”, Int. J. Mod. Phys. A, 34:9 (2019), 1950053
B. A. Arbuzov, I. V. Zaitsev, “Effective couplings and the prospect of solving fundamental problems
of cosmology in a quantum theory of gravity”, Theoret. and Math. Phys., 191:2 (2017), 635–640
Arbuzov B.A., “Effective Interactions and Prospects For Resolution of the Fundamental Cosmological Problems in Quantum Gravity”, Universe, 3:4 (2017), 80
Arbuzov B.A., Zaitsev I.V., “On a possible effective four-boson interaction and its implications at the upgraded LHC”, Prog. Theor. Exp. Phys., 2016, no. 9, 093B02
Arbuzov B.A., Zaitsev I.V., “on a Possibility of a Consistent Interpretation of Diboson Excesses At Lhc”, Mod. Phys. Lett. A, 31:26 (2016), 1650144
Boris A. Arbuzov, Ivan V. Zaitsev, “On a possibility of a consistent interpretation of diboson excesses at LHC”, Mod. Phys. Lett. A, 31:26 (2016), 1650144
Boris A. Arbuzov, Ivan V. Zaitsev, V.A. Andrianov, V.A. Matveev, V.A. Rubakov, V.T. Kim, A.A. Andrianov, M.D. Fitkevich, “Upgraded LHC experiments as a check of non-perturbative effects of the Electro-Weak Interaction”, EPJ Web Conf., 125 (2016), 02002
Arbuzov B.A., Zaitsev I.V., “Atlas Diboson Excesses as An Evidence For a Heavy Ww Resonance With the Weak Isospin 2”, Int. J. Mod. Phys. A, 30:36 (2015), 1550221
Arbuzov B.A., Pitikov A.I., Zaitsev I.V., “Nonperturbative Approach to the Problem of Anomalous Fb Asymmetry in TOP Pair Production at Tevatron”, Int. J. Mod. Phys. A, 28:21 (2013)
Arbuzov B.A. Zaitsev I.V., “On a Possibility to Eliminate the Landau Pole in QCD”, Int. J. Mod. Phys. A, 28:26 (2013)
Bogoslovsky G.Yu., “Dynamic Rearrangement of Vacuum and the Phase Transitions in the Geometric Structure of Space-Time”, Int J Geom Methods Mod Phys, 9:1 (2012), 1250007
Arbuzov B.A., Zaitsev I.V., “CDF W-jj Anomaly as a Nonperturbative Effect of the Electroweak Interaction”, Internat J Modern Phys A, 27:3–4 (2012)
B. A. Arbuzov, “Nonperturbative solutions in the electroweak theory”, Theoret. and Math. Phys., 171:1 (2012), 448–457
Arbuzov B.A., Zaitsev I.V., “Lhc Would-Be Gamma Gamma Excess as a Nonperturbative Effect of the Electroweak Interaction”, Phys. Rev. D, 85:9 (2012), 093001
Arbuzov B.A., Zaitsev I.V., “NONPERTURBATIVE SOLUTIONS IN THE ELECTROWEAK THEORY WITH (t)over-bart CONDENSATE AND THE t-QUARK MASS”, Internat J Modern Phys A, 26:29 (2011), 4945–4958
Arbuzov B.A., Volkov M.K., “Bogoliubov compensation approach in QCD and in the electro-weak theory”, Physics of Particles and Nuclei, 41:6 (2010), 901–904
Arbuzov, BA, “Njl Interaction Derived From QCD: Vector and Axial-Vector Mesons”, International Journal of Modern Physics A, 24:13 (2009), 2415
Arbuzov, BA, “Bogoliubov compensation principle in the electro-weak interaction: value of the gauge constant, muon g-2 anomaly, predictions for Tevatron and LHC”, European Physical Journal C, 61:1 (2009), 51
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