G. Gallavotti

The beta-function method for resummations in field theory

In Constructive quantum field theory II, Ed. G. Velo, A.S. Wightman, Erice, 1988, Nato ASI series B, Physics, vol. 234, 69--88, 1990,
Roma 8/8/1988


This is a concise discussion of a proof of n! bounds on the renormalized series for phi-4 scalar theoriy in 4 dimensions. The analysis is via the renormalizations group and the beta function. As a corollary one obtains the convergence of the planar theory in its expansion in terms of the running coupling constants and its Borel summability inb terms of the renormalized copulings.

Keyword 4-dim scalar field, Quantum fields, Planar field theory, Borel summability, Constructive field theory