Reduction and Reparametrization of Quantum Field Theories

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Abstract
Reductions in coupling parameter space are considered using renormalization group methods. In many (but not all) cases, the reduction to a single parameter λ has only a few special solutions corresponding to theories with renormalized power series expansions in λ. There also exist general solutions with non-integer powers and/or logarithms of λ. They are nevertheless “renormalized” in view of their embedding. The stability of solutions can be discussed using Ljapunov's theorems. Some special solutions of the reduction equations lead to theories with new symmetries, but in the same system one also finds usually non-symmetric solutions. Regular reparametrizations are considered. They are relevant for the reduction and for the calculation of β-functions after reduction. Several examples are reviewed: simple theories with Yukawa- and quartic-couplings, gauge theories with matter couplings, N = 1 supersymmetric theories, calculations of top quark and Higgs couplings.

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