Perturbative renormalization of the lattice regularized $\phi_4^4$ with flow equations

Borji, Majdouline; Kopper, Christoph

doi:10.1063/5.0024211

Perturbative renormalization of the lattice regularized $\phi_4^4$ with flow equations

Jun 29, 2020

24 pages

Published in:

J.Math.Phys. 61 (2020) 11, 112304

Published: Nov 13, 2020

e-Print:

2006.15943 [math-ph]

DOI:

10.1063/5.0024211

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Abstract: (AIP)

The flow equations of the renormalization group allow one to analyze the perturbative n-point functions of renormalizable quantum field theories. Rigorous bounds implying renormalizability permit one to control large momentum behavior, infrared singularities, and large order behavior in a number of loops and a number of arguments n. In this paper, we analyze the Euclidean four-dimensional massive ϕ4 theory using lattice regularization. We present a rigorous proof that this quantum field theory is renormalizable to all orders of the loop expansion based on the flow equations. The lattice regularization is known to break Euclidean symmetry. Our main result is the proof of the restoration of rotation and translation invariance in the renormalized theory using flow equations.

renormalization
perturbation theory
regularization: lattice
phi**n model: 4
field theory: renormalizable
field theory: Euclidean
flow

References(22)

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