Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-04-25
Annals Phys. 241 (1995) 337-367
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, no figures, TeX with harvmac, RAL-94-038, CERN-TH.7233/94
Scientific paper
We consider the infrared and ultraviolet behaviour of the effective quantum field theory of a single $Z_2$ symmetric scalar field. In a previous paper we proved to all orders in perturbation theory the renormalizability of massive effective scalar field theory using Wilson's exact renormalization group equation. Here we show that away from exceptional momenta the massless theory is similarly renormalizable, and we prove detailed bounds on Green's functions as arbitrary combinations of exceptional Euclidean momenta are approached. As a corollary we also prove Weinberg's Theorem for the massive effective theory, in the form of bounds on Green's functions at Euclidean momenta much greater than the particle mass but below the naturalness scale of the theory.
Ball Richard D.
Thorne Robert S.
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