The structure of the invariant charge in massive theories with one coupling
- Institut fuer Theoretische Physik, Universitaet Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
Invariance under finite renormalization group (RG) transformations is used to structure the invariant charge in models with one coupling in the 4 lowest orders of perturbation theory. In every order there starts a RG-invariant, which is uniquely continued to higher orders. Whereas in massless models the RG-invariants are power series in logarithms, there is no such requirement in a massive model. Only when one applies the Callan-Symanzik (CS) equation of the respective theories is the high-energy behavior of the RG-invariants restricted. In models where the CS-equation has the same form as the RG-equation, the massless limit is reached smoothly, i.e., the {beta}-functions are constants in the asymptotic limit and the RG-functions starting the new invariant tend to logarithms. On the other hand, in the spontaneously broken models with fermions the CS-equation contains a {beta}-function of a physical mass. As a consequence the {beta}-functions depend on the normalization point also in the asymptotic region and a mass independent limit does not exist anymore. {copyright} 1995 Academic Press, Inc.
- OSTI ID:
- 165322
- Journal Information:
- Annals of Physics (New York), Vol. 240, Issue 2; Other Information: PBD: Jun 1995
- Country of Publication:
- United States
- Language:
- English
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