Reduced Order Podolsky Model

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.

Reduction of order and Fadeev–Jackiw formalism in generalized electrodynamics

“…which agrees with Eq. (36). We therefore verity that the equivalence between the classical equations of motion in the Ostrogradsky and Reduction of order prescriptions, seen in Eqs.…”

“…Although the (FJ) formalism does not implement major changes in the quantization process of a regular theory, in a singular theory there might be considerable simplifications when adopting the symplectic formalism instead of the usual (DB) algorithm. We apply the (FJ) method to discuss the quantization of the Podolsky electrodynamics [41] but, differently from what was done in [39], we start by writing the theory in the reduction of order formalism, by means of the introduction of an additional auxiliary field B µ , following [36]. We will show that this technique allows us to write the sympletic matrix in a block structure, thus clearly separating the Maxwell and Proca sectors.…”

Computational Model of the Fredholm Method Applied to Podolsky Quantum Wave Function / Modelo Computacional Do Método Fredholm Aplicado À Função Onda Quântica De Podolsky

“…(25) for the scattering region. For this, we will use the technique of the Green function (Suzuki;Sales, 2003;Suzuki;Sales;Carrillo, 2013;Sales;Suzuki, 2013;Thibes, 2017). Thus, being the Green function for Eq.…”

Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

“…We have shown that for even values of N , the homogeneous equation ( 23) has only the trivial solution φ ≡ 0. Also the infinite-order homogeneous equation (26) does not have non-trivial solutions for φ.…”

“…Another interesting path for obtaining higher-derivative models can be seen in [25], where it is shown that nonlocality in space-time via the introduction of forward and back-ward fields can lead to higher-order derivatives with a particular example of a fourth-order generalization of the KG equation given. In this day and age, the study of higher-derivative theories continues to be an active lively field, still containing various chalenging problems and being the main subject of a significative number of works in the most recent literature [26,27,28,29,30,31,32,33,34]. Besides their own mathematical interest, the address of important issues and open questions in physics such as the quantization of gravity and its alternative modified theories, the construction of effective low energy field theories, the dark energy and matter problems and the possibility of Lorentz symmetry breaking at a fundamental level in cosmological models has granted higher-derivative models an important role in the current contemporary physics scenario [35,36,37,38,39].…”