Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
Copyright policy )Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
The paper studies the quantum action for the four-dimensional real $ϕ^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $β$-function is presented. Consistency with previously known results is shown.
LaTeX, 71 pages, 8 figures. Firstly appeared in Russian, February 6, 2024, see https://www.pdmi.ras.ru/preprint/2024/pr2024.html
High Energy Physics - Theory, Renormalization, FOS: Physical sciences, QC770-798, Perturbative methods of renormalization applied to problems in quantum field theory, renormalization, quantum equation of motion, Nuclear and particle physics. Atomic energy. Radioactivity, scalar model, Quantum action, Feynman diagrams, Mathematical Physics, Renormalization constant, quartic interaction, Feynman diagram, deformation, Scalar model, Mathematical Physics (math-ph), Green's function, Renormalization group methods applied to problems in quantum field theory, cutoff regularization, Cutoff regularization, effective action, High Energy Physics - Theory (hep-th), heat kernel, renormalization constant, cutoff momentum, quantum action, three loops
High Energy Physics - Theory, Renormalization, FOS: Physical sciences, QC770-798, Perturbative methods of renormalization applied to problems in quantum field theory, renormalization, quantum equation of motion, Nuclear and particle physics. Atomic energy. Radioactivity, scalar model, Quantum action, Feynman diagrams, Mathematical Physics, Renormalization constant, quartic interaction, Feynman diagram, deformation, Scalar model, Mathematical Physics (math-ph), Green's function, Renormalization group methods applied to problems in quantum field theory, cutoff regularization, Cutoff regularization, effective action, High Energy Physics - Theory (hep-th), heat kernel, renormalization constant, cutoff momentum, quantum action, three loops
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