Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in four-dimensional scalar theories, 2n derivatives of the fields, n > 1, do not appear before the n th loop. A new kind of expansion can be defined to treat functions of the fields ( but not of their derivatives) non-perturbatively. I study the conditions under which these theories can be consistently renormalized with a reduced, eventually finite, set of independent couplings. I find that in common models the number of couplings sporadically grows together with the order of the expansion, but the growth is slow and a reasonably small number of couplings is sufficient to make predictions up to very high orders. Various examples are solved explicitly at one and two loops.
|Titolo:||Renormalization of a class of non-renormalizable theories|
|Anno del prodotto:||2005|
|Digital Object Identifier (DOI):||10.1088/1126-6708/2005/07/077|
|Appare nelle tipologie:||1.1 Articolo in rivista|