The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU (2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. The diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component of the gluon propagator is found to be of the Yukawa type, with a dynamical mass originating from the dimension two condensate A a µ A a µ , which is also taken into account. Finally, the off-diagonal ghost propagator exhibits infrared enhancement. * marcio@dft.if.uerj.br † vitor@dft.if.uerj.br ‡ sobreiro@uerj.br § sorella@uerj.br ¶ Work supported by FAPERJ, Fundação de Amparoà Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/151.947/2004. thibes@dft.if.uerj.br

We pursue the study of SU (2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [1], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U (1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z g Z *

The infrared behavior of the gluon and ghost propagators is studied in SU (2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data. * marcio@dft.if.uerj.br † vitor@dft.if.uerj.br ‡ sobreiro@cbpf.br § sorella@uerj.br ¶ Work supported by FAPERJ, Fundação de Amparoà Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/100.615/2007. thibes@dft.if.uerj.br

A class of covariant gauges allowing one to interpolate between the Landau, the maximal Abelian, the linear covariant and the Curci-Ferrari gauges is discussed. Multiplicative renormalizability is proven to all orders by means of algebraic renormalization. All one-loop anomalous dimensions of the fields and gauge parameters are explicitly evaluated in the MS scheme.

We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale Λ, i.e. a = 1/Λ. Solving explicitly the classical static Bopp-Podolsky's equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics. arXiv:1902.07632v1 [hep-th]