Wilson RG of noncommutative Φ44

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N. Three fixed points are identified. The matrix model [Formula: see text] fixed point which describes the disordered-to-nonuniform-ordered transition. The Wilson–Fisher fixed point at [Formula: see text] which describes the disordered-to-uniform-ordered transition, and a noncommutative Wilson–Fisher fixed point at a maximum value of [Formula: see text] which is associated with the transition between nonuniform-order and uniform-order phases.

WILSON RENORMALIZATION GROUP FOR GAUGE THEORIES

The Wilson renormalization group formulation of gauge theories is reviewed. In particular, the fine tuning procedure needed to recover the gauge invariance broken by the infrared cutoff is discussed. When the cutoff is larger than any physical scale, this procedure determines the finite non-invariant couplings of the ultraviolet action. These couplings are used to build up a local field transformation which allows to write a BRS invariant ultraviolet action.

RENORMALIZATION OF HAMILTONIAN

In this talk we describe a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group1. By a series of unitary transformations that successively decouple the high-frequency degrees of freedom and partially diagonalizes the high-energy part, we obtain the effective Hamiltonian for the low energy degrees of freedom. Using this technique we study λϕ4 theory at two loops and QED and Yang-Mills theory at one loop.

GAUGE CONSISTENT WILSON RENORMALIZATION GROUP I: THE ABELIAN CASE

A version of the Exact Renormalization Group Equation consistent with gauge symmetry is presented. A discussion of its regularization and renormalization is given. The relation with the Callan–Symanzik equation is clarified.

GAUGE CONSISTENT WILSON RENORMALIZATION GROUP II: THE NON-ABELIAN CASE

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed.