A self-contained analysis is given of the simplest quantum fields from the renormalization group point of view: multiscale decomposition, general renormalization theory, resummations of renormalized series via equations of the Callan-Symanzik type, asymptotic freedom, and proof of ultraviolet stability for sine-Gordon fields in two dimensions and for other super-renormalizable scalar fields. Renormalization in four dimensions (Hepp's theorem and the De Calan-Rivasseau n! bound) is presented and applications are made to the Coulomb gases in two dimensions and to the convergence of the planar graph expansions in four-dimensional field theories (t' Hooft-Rivasseau theorem). © 1985 The American Physical Society.
Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods / Gallavotti, Giovanni. - In: REVIEWS OF MODERN PHYSICS. - ISSN 0034-6861. - STAMPA. - 57:2(1985), pp. 471-562. [10.1103/revmodphys.57.471]
Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
GALLAVOTTI, Giovanni
1985
Abstract
A self-contained analysis is given of the simplest quantum fields from the renormalization group point of view: multiscale decomposition, general renormalization theory, resummations of renormalized series via equations of the Callan-Symanzik type, asymptotic freedom, and proof of ultraviolet stability for sine-Gordon fields in two dimensions and for other super-renormalizable scalar fields. Renormalization in four dimensions (Hepp's theorem and the De Calan-Rivasseau n! bound) is presented and applications are made to the Coulomb gases in two dimensions and to the convergence of the planar graph expansions in four-dimensional field theories (t' Hooft-Rivasseau theorem). © 1985 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.