A description of how to define in a mathematically rigorous way the beta function, well known from the nonrigorous perturbative formulation of quantum field theory. The definition is based on a kind of effective potentials, for which a "tree expansion'' is proposed. It is also described how to use such a beta function in order to rigorously construct a model which is renormalizable and asymptotically free (but not super-renormalizable model). The paper also contains a discussion of applicability of the tree expansion in statistical mechanics.
Renormalization Theory and Group in Mathematical Physics / Gallavotti, Giovanni. - STAMPA. - (1988), pp. 1268-1277. (Intervento presentato al convegno ICM Berkeley 1986 tenutosi a Berkeley nel 3-11 August 1986).
Renormalization Theory and Group in Mathematical Physics
GALLAVOTTI, Giovanni
1988
Abstract
A description of how to define in a mathematically rigorous way the beta function, well known from the nonrigorous perturbative formulation of quantum field theory. The definition is based on a kind of effective potentials, for which a "tree expansion'' is proposed. It is also described how to use such a beta function in order to rigorously construct a model which is renormalizable and asymptotically free (but not super-renormalizable model). The paper also contains a discussion of applicability of the tree expansion in statistical mechanics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
