arXiv subjects

Ronaldo Thibes

Publications and source records attributed to Ronaldo Thibes.

30 records · Page 2Linked to original sources

arXiv2022

BFV quantization and BRST symmetries of the gauge invariant fourth-order Pais-Uhlenbeck oscillator

We perform the BFV-BRST quantization of the fourth-order Pais-Uhlenbeck oscillator (PUO). We show that although the PUO is not naturally constrained in the sense of Dirac-Bergmann, it is possible to profit from the introduction of suitable constraints in phase space in order to obtain a proper BRST invariant quantum system. Starting from its second-class constrained system description, we use the BFFT conversional approach to obtain first-class constraints as gauge symmetry generators. After the Abelianization of the constraints, we obtain the conserved BRST charge, the corresponding BRST transformations and proceed further to the BFV functional quantization of the model. We show that different possible gauge choices can be connected by finite field-dependent BRST transformations.

hep-th↗

arXiv2021

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second- to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for applications to mechanical models as well as field theory such as the non-linear sigma model. The constraints can be arbitralily non-linear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As explicit examples, we discuss a particle on a torus and a spontaneous Lorentz symmetry breaking vector model, obtaining in both situations the full first-class abelianized constraints in closed form and the corresponding involutive Hamiltonian.

hep-th↗

arXiv2020

Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing higher-derivative terms. The limit obtained by considering arbitrarily higher-order powers of the d'Alembertian operator leading to a formal infinite-order partial differential equation is discussed. The general model is constructed using the exponential of the d'Alembertian differential operator. The canonical energy-momentum tensor densities and field propagators are explicitly computed. We consider both homogeneous and non-homogeneous situations. The classical solutions are obtained for all cases.

math-ph↗

arXiv2020

BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We pursue the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the $O(N)$ nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

hep-th↗

arXiv2020

Bopp-Podolsky Scalar Electrodynamics Propagators and Energy-Momentum Tensor in Covariant and Light-Front Coordinates

We consider the interaction between a charged scalar boson and the Bopp-Podolsky gauge fields. The Bopp-Podolsky (BP) electrodynamics possesses both massive and massless propagation modes for the photon, while preserving gauge invariance. We obtain the propagator of all fields present in the model for the higher-order generalizations of the linear covariant, light-front and doubly transverse light-front gauges. Although BP's original model is described by a higher-order derivatives Lagrangian, it is possible to work with an equivalent reduced-order version by means of the introduction of an auxiliary vector field. We compute the gauge-invariant improved energy-momentum tensor for the full reduced-order interacting BP model. Besides the more traditional front-form view, we also discuss the light-front perspective in both versions of the model. Within a Lagrangian framework approach we maintain explicit covariance at all steps and show that the field propagators, as well as the energy-momentum tensor, can be cast into a light-front closed form using specific properties of general coordinate transformations.

hep-th↗

arXiv2019

First-Order Gauge Invariant Generalization of the Quantum Rigid Rotor

A first-order gauge invariant formulation for the two-dimensional quantum rigid rotor is long known in the theoretical physics community as an isolated peculiar model. Parallel to that fact, the longstanding constraints abelianization problem, aiming at the conversion from second to first class systems for quantization purposes, has been approached a number of times in the literature with a handful of different forms and techniques and still continues to be a source of lively and interesting discussions. Connecting these two points, we develop a new systematic method for converting second class systems to first class ones, valid for a class of systems encompassing the quantum rigid rotor as a special case. In particular the gauge invariance of the quantum rigid rotor is fully clarified and generalized in the context of arbitrary translations along the radial momentum direction. Our method differs substantially from previous ones as it does not rely neither on the introduction of new auxiliary variables nor on the a priori interpretation of the second class constraints as coming from a gauge-fixing process.

hep-th↗

arXiv2019

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 $Λ$, 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.

hep-th↗

arXiv2017

Conic Constrained Particle Quantization within the DB, FJBW and BRST Approaches

We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum counterpart with subtleties in its symplectic structure and symmetries. The model is used here to investigate quantization issues related to the Hamiltonian constraint structure, Dirac brackets, gauge symmetry and BRST transformations. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the fine tuned and more relevant aspects of the constraint structure. A comparison with the longer usual Dirac-Bergmann algorithm, still more well established in the literature, is also presented. While in the standard DB approach there are four second class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process we construct a gauge invariant model exhibiting explicitly its BRST symmetry. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor showing that it constitutes a particular case of a broader class of theories.

hep-th↗

arXiv2016

Revisiting fermion helicity flip in Podolsky's Electromagnetism

The spin projection of a massive particle onto its direction of motion is called helicity (or "handedness"). It can therefore be positive or negative. When a particle's helicity changes from positive to negative (or vice-versa) due to its interaction with other particles or fields, we say there is a helicity flip. In this work we show that such helicity flip can be seen for an electron of $20 MeV$ of energy interacting with a charged scalar meson through the exchange of a virtual photon. This photon {\it does not} necessarily need to be Podolsky's proposed photon; in fact, it is independent of it.

hep-ph↗

arXiv2016

Reduced Order Podolsky Model

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.

hep-th↗

arXiv1999

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.

hep-th↗

arXiv1997

Possible quantum obstructions to the process of Abelian conversion

The procedure for Abelian conversion of second class constraints due to Batalin, Fradkin, Fradkina and Tyutin is considered at quantum level, by using the field-antifield formalism. It is argued that quantum effects can obstruct the process. In this case, Wess-Zumino fields may be introduced in order to restore the lost symmetries.

hep-th↗