Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
Journal Article
·
· Rev. Mod. Phys.; (United States)
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 nexclamation 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).
- Research Organization:
- Dipartimento di Matematica, II Universita di Roma, Via O. Raimondo, 00173 Roma, Italy
- OSTI ID:
- 5758212
- Journal Information:
- Rev. Mod. Phys.; (United States), Journal Name: Rev. Mod. Phys.; (United States) Vol. 57:2; ISSN RMPHA
- Country of Publication:
- United States
- Language:
- English
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