Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods

  title={Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods},
  author={Giovanni Gallavotti},
  journal={Reviews of Modern Physics},
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… Expand

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