Massive and massless spin-1 particles with gauge symmetry without Stueckelberg fields
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Regular Article - Theoretical Physics
Massive and massless spin-1 particles with gauge symmetry without Stueckelberg fields D. Dalmazia UNESP, Campus de Guaratinguetá, DFQ, Avenida Doutor Ariberto Pereira da Cunha, 333, CEP 12516-410, Guaratinguetá, SP, Brazil
Received: 26 June 2012 / Revised: 27 July 2012 © Springer-Verlag / Società Italiana di Fisica 2012
Abstract In order to generate mass for an abelian spin-1 vector field while preserving gauge invariance we couple it to a symmetric tensor. The derivative coupling includes up to three derivatives. We show that unitarity, causality and absence of Stueckelberg (compensating) fields single out a unique model up to trivial field redefinitions. The model contains one massive and one massless spin-1 particle. It is shown by means of a master action to be dual to the direct sum of a Maxwell plus a Maxwell–Proca theory.
1 Introduction The key feature of the Higgs mechanism [1–3] is to provide mass for spin-1 particles without abandoning the gauge invariance principle which is crucial for the standard model. Another well known mechanism to preserve gauge symmetry while generating mass for vector bosons is to introduce pure gauge compensating (Stueckelberg) fields, see e.g. [4] for a review. The Higgs mechanism must be confirmed by the existence of the Higgs particle while the Stueckelberg approach apparently cannot be extended to the nonabelian case without spoiling renormalizability. A rare example of a model for a massive vector field with gauge symmetry which avoids the above mentioned mechanisms is the topologically massive BF model (TMBF) also known as Cremmer–Scherk model [5–7]. In this case instead of interacting with scalar fields, the massless vector field acquires mass from a topological coupling to an antisymmetric tensor. The antisymmetric tensor plays the role of an auxiliary field which can be eliminated in favor of the vector field which becomes massive. After integration over the antisymmetric tensor, the effective Lagrangian density for the massive vector field is of the Schwinger type, i.e., L ∼ Fμν (1 − m2 /)F μν , see [8]. Unfortunately, a nonabelian renormalizable generalization of the TMBF model a e-mail:
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can be hardly obtained, see [9, 10], unless one introduces extra fields [11–14]. The origin of the TMBF model may be traced back to a first-order (in derivatives) version of the Maxwell theory in terms of an antisymmetric tensor. Inspired by another firstorder version of the Maxwell theory [15] which replaces the antisymmetric tensor by a symmetric one we have investigated in [16] the coupling of the vector field to a symmetric tensor as a mass generation mechanism which preserves gauge symmetry. Starting with a second-order action in derivatives we have shown that the symmetric tensor can indeed provide mass for the vector field without contributing itself as a physical degree of freedom similarly to the TMBF model. In particular, after integration over the symmetric tensor the effective action for the vector field is
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