Banca de QUALIFICAÇÃO: EDUARDO LOURENÇO FÁBIO DE LIMA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE : EDUARDO LOURENÇO FÁBIO DE LIMA
Data: 13/08/2026
HORA: 14:00
LOCAL: Videoconferência
TÍTULO:

Regular Canonical Representations of Snyder–de Siter Poisson Algebra and Aplications

PÁGINAS: 49
RESUMO:

Snyder--de Sitter phase space provides a Lorentz-covariant framework in which ultraviolet noncommutativity and infrared curvature effects are incorporated simultaneously through two deformation parameters, ($\beta$) and ($\alpha$). This structure is physically appealing because it combines the Snyder idea of a fundamental length scale with a de Sitter-type deformation of momentum space. However, its nonlinear Poisson algebra also creates a central difficulty: the phase space is noncanonical, the Poisson tensor is coordinate-dependent, and many known Darboux representations contain singular ratios such as ($\alpha/\beta$) or ($\beta/\alpha$). As a consequence, the Snyder, de Sitter, and canonical limits cannot be treated in a unified and regular way. In this work, we address this problem of the singular ratios by developing a nonperturbative (Exact solution) formulation of the Snyder--de Sitter phase space directly from its Poisson tensor. Rather than assuming a Darboux map from the beginning, we invert the Poisson tensor, construct the corresponding symplectic form, and derive a closed-form symplectic potential using the Poincaré operator. This intrinsic construction leads to a regular Darboux representation whose coefficients depend only on invariant scalar combinations of the phase-space variables. The resulting map contains no singular ratios between the deformation parameters and admits smooth Snyder, de Sitter, and canonical limits. In the Snyder limit, the representation admits a clear geometric interpretation as a radial deformation of momentum space together with a transverse-longitudinal rescaling of the position variables. Finally, we construct an explicit nontrivial canonical transformation relating our Snyder-limit Darboux map to the standard Snyder chart used in the literature. Thus, the framework developed here provides a regular symplectic foundation for deformed classical dynamics, quantum mechanics, harmonic oscillator models, and future developments in Snyder--Poisson gauge theory.

MEMBROS DA BANCA:
Presidente - Interno ao Programa - 2616823 - ALYSSON FABIO FERRARI
Membro Titular - Examinador(a) Interno ao Programa - 1545176 - MARCELO AUGUSTO LEIGUI DE OLIVEIRA
Membro Titular - Examinador(a) Interno ao Programa - 1768463 - OLEXANDR ZHYDENKO
Membro Suplente - Examinador(a) Interno ao Programa - 1574260 - ROLDAO DA ROCHA JUNIOR