The Standard Model and its Generalisations in Epstein-Glaser Approach to Renormalisation Theory

Abstract

We continue our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalisation theory. We consider the case when massive spin-one Bosons are present into the theory and we modify appropriately the analysis of the origin of gauge invariance performed in a preceding paper in the case of null-mass spin-one Bosons. Then we are able to extend a result of Dütsch and Scharf concerning the uniqueness of the standard model consistent with renormalisation theory. In fact we consider the most general case i.e. the consistent interaction of $r$ spin-one Bosons and we do not impose any restriction on the gauge group and the mass spectrum of the theory. We show that, beside the natural emergence of a group structure (like in the massless case) we obtain, new conditions of group-theoretical nature, namely the existence of a certain representation of the gauge group associated to the Higgs fields. Some other mass relations connecting the structure constants of the gauge group and the masses of the Bosons emerge naturally. The proof is done using Epstein-Glaser approach to renormalisation theory.

42 pages, LATEX 2e, some improvements and corrections

References in corpus (6)

• The Renormalization of the Electroweak Standard Model to All Orders
• Non-abelian gauge theories as a consequence of perturbative quantum gauge invariance
• Massive Vector Mesons and Gauge Theory
• Quantum Noether Method
• Gauge Independence of the S-Matrix in the Causal Approach
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• The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
• Massive Supersymmetric Quantum Gauge Theory
• Massive vector bosons: is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?
• Spontaneous emission and atomic line shift in causal perturbation theory
• The Interaction of Quantum Gravity with Matter