Reduction of order and Fadeev–Jackiw formalism in generalized electrodynamics

Nogueira, A.A.  (Universidade Federal de Goias, Instituto de Física, Av. Esperanca, Goiânia, Goiás, 74690-900, Brasil) (Universidade Federal do ABC, Centro de Ciências Naturais e Humanas, Rua Santa Adélia, 166, Santo André, SP, 09210-170, Brasil) ; Palechor, C. (Universidade Federal do ABC, Centro de Ciências Naturais e Humanas, Rua Santa Adélia, 166, Santo André, SP, 09210-170, Brasil) ; Ferrari, A.F. (Universidade Federal do ABC, Centro de Ciências Naturais e Humanas, Rua Santa Adélia, 166, Santo André, SP, 09210-170, Brasil) (Indiana University Center for Spacetime Symmetries, Indiana University, Bloomington, IN, 47405-7105, United States of America)

28 December 2018

Abstract: The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev–Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a regular theory (a higher derivative massless scalar theory), both using the Ostrogradsky prescription and also by reducing the order of the Lagrangian with an auxiliary field, showing the equivalence of these two approaches. The interpretation of the degrees of freedom is discussed in some detail. Finally, we perform the similar analysis in a singular higher derivative gauge theory (the Podolsky electrodynamics), in the reduced order formalism: we claim that this approach have the advantage of clearly separating the symplectic structure of the model into a Maxwell and a Proca (ghost) sector, thus complementing the understanding of the degrees of freedom of the theory and simplifying calculations involving matrices.


Published in: Nuclear Physics B 939 (2019) 372-390
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2018.12.026
License: CC-BY-3.0



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