par Adler, Stephen L;Henneaux, Marc 
;Pais Hirigoyen, Pablo
Référence Physical Review D - Particles, Fields, Gravitation and Cosmology, 96, 8, 085005
Publication Publié, 2017-10-16
;Pais Hirigoyen, Pablo Référence Physical Review D - Particles, Fields, Gravitation and Cosmology, 96, 8, 085005
Publication Publié, 2017-10-16
Article révisé par les pairs
| Résumé : | We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension 12 auxiliary spin-12 field Λ, in which there is an exact off-shell gauge invariance. In Λ=0 gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semidefinite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semidefinite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension 32 spin-12 fields. |
