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Perturbative renormalization of the lattice regularized \(\phi_4^4\) with flow equations. (English) Zbl 1454.81149
Summary: 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 \(\varphi^4\) 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.
©2020 American Institute of Physics
MSC:
81T17 Renormalization group methods applied to problems in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
81T25 Quantum field theory on lattices
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