The generalized electrodynamics proposed by Podolsky is analyzed from the Hamiltonian point of view, using Dirac theory for constrained systems. The problem of gauge fixing for the theory is studied in detail and the correct generalization of the radiation gauge is obtained, a subject that has not been examined correctly in the earlier literature. The Dirac brackets for the dynamical variables in this gauge are calculated.

Two problems relative to the electromagnetic coupling of Duffin-Kemmer-Petiau (DKP) theory are discussed: the presence of an anomalous term in the Hamiltonian form of the theory and the apparent difference between the Interaction terms in DKP and Klein-Gordon (KG) Lagrangians. For this, we first discuss the behavior of DKP field and its physical components under gauge transformations.From this analysis, we can show that these problems simply do not exist if one correctly analyses the physical components of DKP field.

The conformal affine sl(2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry. Academic Press

In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximation of all Green's functions and a discussion about the obtained results are presented. * rbufalo@ift.unesp.br † pimentel@ift.unesp.br ‡ gramos@udenar.edu.co [3]. Also, the use of higher derivative terms becomes interesting regulatorr, by the fact that it improves the convergence of the Feynman diagrams [4].More examples of systems treated with high-order Lagrangians that we can mention are: the study of the problem of color confinement on the infrared sector of QCD 4 [5], the attempts to solve the problem of renormalization of the gravitational field [6], and a generalization of Utiyma's theory to second-order theories [7]. Although all these works improve the use of higher-order terms, the ones that most contributed to show the effectiveness of such terms in field theory was the contributions of Bopp [8], and Podolsky and Schwed [9], where they proposed a generalization of the Maxwell electromagnetic field. They wanted to get rid of the infinities of the theory, such as the electron self-energy (r −1 singularity) and the vacuum polarization current present on the Maxwell theory. The modification suggested by Podolsky and Schwed handle these unsolved problems and, also, gives a positive definite energy in the electrostatic case; also, as showed by Frenkel [10], it gives the correct expression for the self-force of charged particles. In [7], it was shown that the Podolsky Lagrangian is the only possible generalization of Maxwell electrodynamics that preserves invariance under U (1).On theoretical and experimental framework, efforts have been made to determine an upper-bound value for the mass of the photon [11], the existence of a massive sector being a prediction of generalized electrodynamics. Along this line of thought, we believe that a way to set limits over Podolsky parameter will be to study the Podolsky's photons interacting with standard model particles, and compare the obtained results with high-energy experiments. This idea and other purposes led Podolsky and some of his students to study the interaction of electrons with the Podolsky photons, which they called generalized quantum electrodynamics (GQED 4 ) [12]. Among the points dealt with in their thesis, the most interesting was the calculation of electron self-energy at a one-loop approximation. They expected that the contribution of massive photons lead to a finite result; nevertheless, in the end, they found, as in the usual QED 4 , a divergent expression. Analyzing, now, the thesis results, we found a mistake in their tr...

In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics (GQED4). We begin the article by reviewing the on-shell renormalization scheme applied to GQED4. Thereafter, we calculate the explicit expressions for all the counter-terms at one-loop approximation and discuss the infrared behavior of the theory as well. Next, we explore some properties of the effective coupling of the theory which would give an indictment of the validity regime of theory: m 2 ≤ k 2 < m 2 P . Afterwards, we make use of experimental data from the electron anomalous magnetic moment to set possible values for the theory free parameter through the one-loop contribution of Podolsky mass-dependent term to Pauli's form factor F2 q 2 .

a b s t r a c tIn this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space.

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the HamiltonJacobi equation for such systems, analizing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared.