Renormalization: an advanced overview

Abstract

We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods à la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.

Review, 130 pages, 33 figures; v2: misprints corrected, refs. added, minor improvements; v3: some changes to sect. 5, refs. added

References in corpus (6)

• Introduction to Effective Field Theory
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Constructive ${\varphi }^4$ field theory without tears
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Generalized constructive tree weights
• The Multiscale Loop Vertex Expansion

Cited by in corpus (13)

• The critical O(N) CFT: Methods and conformal data
• The Tensor Theory Space
• Constructive Tensor Field Theory
• Group Field Theory in dimension four minus epsilon
• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
• Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups
• Open Spin Chains and Complexity in the High Energy Limit
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Tensor Field Theories: Renormalization and Random Geometry
• One-matrix differential reformulation of two-matrix models
• Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0