Abstract
We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky’s generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky’s original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.
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Acknowledgments
The author thanks Prof. Chueng-Ryong Ji for enlightening physical discussions on the subject and gratefully appreciates kind hospitality from the Physics Department at North Carolina State University during postdoctoral research visit which made this work possible. Financial support from the Brazilian funding agency Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq under process number 202141/2015-2 is acknowledged.
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Thibes, R. Reduced Order Podolsky Model. Braz J Phys 47, 72–80 (2017). https://doi.org/10.1007/s13538-016-0475-7
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DOI: https://doi.org/10.1007/s13538-016-0475-7