Polchinski Equation Research Articles

O( N) models within the local potential approximation

Using the Wegner-Houghton equation, within the local potential approximation, we study critical properties of O( N) vector models. Fixed points, together with their critical exponents and eigenoperators, are obtained for a large set of values of N, including N = 0 and N → ∞. Polchinski's equation is also treated. The peculiarities of the large N limit, where a line of Fixed Points at d = 2 + 2/ n is present, are studied in detail. A derivation of the equation is presented together with its projection to zero-modes.

Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case

A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the “relevant” vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.