Geodesic
Spontaneous Generation of Effective Interaction in a~Renormalizable Quantum Field Theory Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 367-387

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We consider the theory of a massless scalar field $\phi$ with the $g\phi^3$ 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 $G\phi^4$ 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 $\phi$ 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 the$g \phi^3$ 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, nontrivial solution.
Mots-clés : compensation equation 
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     author = {B. A. Arbuzov},
     title = {Spontaneous {Generation} of {Effective} {Interaction} in {a~Renormalizable} {Quantum} {Field} {Theory} {Model}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {367--387},
     publisher = {mathdoc},
     volume = {140},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_3_a1/}
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B. A. Arbuzov. Spontaneous Generation of Effective Interaction in a~Renormalizable Quantum Field Theory Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 367-387. http://geodesic.mathdoc.fr/item/TMF_2004_140_3_a1/