Eur. Phys. J. C 69, 599-621 (2010)
https://doi.org/10.1140/epjc/s10052-010-1432-1

Quantum gauge models without (classical) Higgs mechanism

¹ Courant Research Center “Higher order structures in Mathematics”, Mathematisches Institut, Univ. Göttingen, 37073, Göttingen, Germany
² Departamento de Física Teórica, Universidad de Zaragoza, Zaragoza, 50009, Spain
³ Institut für Physik, Theoretische Elementarteilchenphysik, Johannes Gutenberg-Universität, 55099, Mainz, Germany
⁴ Escuela de Matemática, Universidad de Costa Rica, San José, 2060, Costa Rica

jmgb@unizar.es

Received: 14 June 2010
Revised: 19 August 2010
Published online: 15 September 2010

Abstract

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein–Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(–Englert–Brout–Guralnik–Hagen–Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.