Abstract:
The paper studies the quantum action for the three-dimensional real theory $\phi^6$ using the background field method. Three-loop renormalization is performed with a cutoff regularization in the coordinate representation. An explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions is discussed.
Key words and phrases:renormalization, renormalization constant, scalar model, cutoff regularization, Green's function, quantum action, quantum equation of motion, Feynman diagram, three loops, effective action, deformation, hexic interaction.
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