On the BFFT quantization of first order systems

By using the field-antifield formalism, we show that the method of Batalin, Fradkin, Fradkina and Tyutin to convert Hamiltonian systems submitted to second class constraints introduces compensating fields which do not belong to the BRST cohomology at ghost number one. This assures that the gauge symmetries which arise from the BFFT procedure are not obstructed at quantum level. An example where massive electrodynamics is coupled to chiral fermions is considered. We solve the quantum master equation for the model and show that the respective counterterm has a decisive role in extracting anomalous expectation values associated with the divergence of the Noether chiral current.Comment: 18 pages, LaTeX, no figures, to appear in Journal of Mathematical Physic

Pauli-Villars Regularization Elucidated in Bopp-Podolsky's Generalized Electrodynamics

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 $\Lambda$, i.e. $a = 1/\Lambda$. 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

Small mass graviton propagator via finite-field-dependent BRST transformations in the critical dimension Siegel-Zwiebach action from string theory

We discuss the divergent graviton propagator massless limit problem in $D=26$ and show how it can be rigorously approached by interconnecting distinct gauge-fixed Siegel-Zwiebach generating functionals from string theory in the critical dimension through proper finite-field-dependent BRST (FFBRST) transformations. The massive Fierz-Pauli Lagrangian can be obtained from the gauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case, however suffering from the van Dam-Veltman-Zakharov discontinuity and possessing a ill-defined propagator in the massless limit. Nevertheless, alternatively working in a more suitable generalized Lorenz type gauge, including the transverse-traceless case, the graviton propagator for the Siegel-Zwiebach Lagrangian in the massless limit can be made finite. Gauge attainability and nilpotent BRST symmetries are explicitly worked out. We write down the complete corresponding generating functional, including the ghosts sector, and construct a convenient FFBRST transformation connecting the unitary gauge to a new bi-parametrized class of gauge-fixings containing the transverse traceless case. By taking into account the corresponding change in the Feynman integral Jacobian, a finite massless continuous limit propagator is achieved and fully justified

New Forms of BRST Symmetry on a Prototypical First-Class System

We scrutinize the many known forms of BRST symmetries, as well as some new ones, realized within a prototypical first-class system. Similarities and differences among ordinary BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetries are highlighted and discussed. We identify a precise $\mathbb{Z}_4\times\mathbb{Z}_2$ discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST transformations. Considering a Hamiltonian approach, those symmetries can be interrelated by canonical transformations among ghost variables. However, the distinguished characteristic role of the dual BRST symmetries can be fully appreciated within a gauge-fixed Lagrangian viewpoint. New forms of BRST symmetries are given, a set generalizing particular ones previously reported in the literature as well as a brand new unprecedented set. The featured gauge invariant prototypical first-class system encompasses an extensive class of physical models and sheds light on previous controversies in the current quantum field theory literature.Comment: 12 pages, No Figs, Late