Abstract
We investigate Symanzik's improvement program in a four-dimensional Euclidean scalar field theory with smooth momentum space cutoff. We use Wilson's renormalization group transformation to define the improved actions as a sequence of initial data for the effective action at the fundamental cutoff. This leads to a sequence of solutions to the renormalization group equation. We define the parameters of the improved actions implicitly by conditions on the effective action at a renormalization scale. The improved actions are close approximations to the continuum effective action. We prove their existence to every order of improvement and to every order of renormalized perturbation theory.
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Communicated by A. Jaffe
Supported in part by a German National Scholarship Foundation fellowship, and by the National Science Foundation under Grant DMS/PHY 86-45122
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Wieczerkowski, C. Symanzik's improved actions from the viewpoint of the renormalization group. Commun.Math. Phys. 120, 149–176 (1988). https://doi.org/10.1007/BF01223210
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DOI: https://doi.org/10.1007/BF01223210