Perturbative renormalization of the lattice regularized ${\varphi }_4^4$ with flow equations

Abstract

The flow equations of the renormalization group allow to analyse the perturbative $n$-point functions of renormalizable quantum filed theories. Rigorous bounds implying renormalizability permit to control large momentum behaviour, infrared singularities and large order behaviour in the number of loops and the number of arguments $n$. In this paper, we analyse the Euclidean $4$-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 is known to break the Euclidean symmetry of the space-time. Our main result is the proof of the restoration of the Euclidean symmetries using the flow equations.

References in corpus (7)

• Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories
• Perturbative Renormalization by Flow Equations
• Temperature Independent Renormalization of Finite Temperature Field Theory
• Renormalization of SU(2) Yang-Mills theory with Flow Equations
• Perturbative Renormalization with Flow Equations in Minkowski Space
• Renormalization of Matter Field Theories on the Lattice and the Flow Equation
• Mean field flow equations and asymptotically free scalar fields

Cited by in corpus (2)

• Perturbative renormalization of ${\varphi }_4^4$ theory on the half space ${\mathbb{R}}^{+}\times {\mathbb{R}}^3$ with flow equations
• Landau Theory of Causal Dynamical Triangulations