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 .

In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.

In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the nullplane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and proper conditions must be chosen on the null-planes. We will show that the constraint structure, based on Dirac formalism, presents a set of second-class constraints, which are exclusive of the analysis on the null-plane, and an expected set of first-class constraints that are generators of a U (1) group of gauge transformations. An inspection on the field equations will lead us to the generalized radiation gauge on the null-plane, and Dirac Brackets will be introduced considering the problem of uniqueness of these brackets under the chosen initial-boundary condition of the theory. * mcbertin@ift.unesp.br. †

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory.