arXiv subjects

Elisabeth Kraus

Publications and source records attributed to Elisabeth Kraus.

23 records · Page 2Linked to original sources

arXiv1996

Gauge parameter dependence and gauge invariance in the Abelian Higgs model

We analyze gauge parameter dependence by using an algebraic method which relates the gauge parameter dependence of Green functions to an enlarged Slavnov-Taylor identity. In the course of the renormalization it turns out that gauge parameter dependence of physical parameters is already restricted at the level of Green functions. In a first step we consider the on-shell conditions which we find to be in complete agreement with these restrictions to all orders of perturbation theory. The fixing of the coupling, however, is much more involved outside the complete on-shell scheme. In the Abelian Higgs model we prove that this fixing can be properly chosen by requiring the Ward identity of gauge invariance to hold in its tree form to all orders of perturbation theory.

hep-th↗

arXiv1996

The standard model in the on-shell scheme

We outline the renormalization of the standard model to all orders of perturbation theory in a way which does not make essential use of a specific subtraction scheme but is based on the Slavnov-Taylor identity. Physical fields and parameters are used throughout the paper. The Ward-identity for the global gauge invariance of the vertex functions is formulated. As an application the Callan-Symanzik equation is derived.

hep-th↗

arXiv1995

Rigid invariance as derived from BRS invariance: The abelian Higgs model

Consequences of a symmetry, e.g.\ relations amongst Green functions, are renormalization scheme independently expressed in terms of a rigid Ward identity. The corresponding local version yields information on the respective current. In the case of spontaneous breakdown one has to define the theory via the BRS invariance and thus to construct rigid and current Ward identity non-trivially in accordance with it. We performed this construction to all orders of perturbation theory in the abelian Higgs model as a prelude to the standard model. A technical tool of interest in itself is the use of a doublet of external scalar ``background'' fields. The Callan-Symanzik equation has an interesting form and follows easily once the rigid invariance is established.

hep-th↗

arXiv1994

Asymptotic normalization properties and mass independent renormalization group functions

Mass independent renormalization group functions in massive theories are related to normalization properties of the Green functions in the asymptotic region, where mass effects are neglected. In this special form the renormalization group invariance is restricted to the asymptotic region and consequently mass effects cannot be recoverd by a integration of the renormalziation group equation. It is shown, that mass independence results in the limit of a large normalization point, whenever a Callan-Symanzik equation exists and contains the same differential operators as the renormalization group equation.

hep-th↗

arXiv1993

The structure of the invariant charge in massive theories with one coupling

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, the high-energy behavior of the RG-invariants is 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.

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