Noncommutative Gauge Dynamics from L_infinity- Algebras

• Grant number: 24/23831-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2025
• End date: February 29, 2028
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Vladislav Kupriyanov
• Grantee: Eduardo Lourenço Fabio de Lima
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Santo André , SP, Brazil

Abstract

Non-commutative (NC) gauge theories on coordinate-dependent space-time provide a robust framework to investigate deviations from classical physics, particularly when the non-commutativity parameter $\Theta^{ab}(x)$ varies with space-time coordinates. Using the $L_\infty$-algebra formalism, these theories encode higher-order corrections and ensure consistency through generalized Jacobi identities. This project extends the graded vector space $V = V_0 \oplus V_1$ to include $V_2$, the field strength tensor $\mathcal{F}_{\mu\nu}$ is incorporated, capturing the dynamical content of NC gauge theories. The $L_\infty$-bootstrap method systematically constructs these deformations, maintains gauge covariance, and ensures algebraic closure. This unified formalism provides a powerful tool to explore the algebraic, geometric, and physical implications of NC gauge theories.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KUPRIYANOV, V. G.; DE LIMA, E. L. F.. Symplectic Realization of Generalized Snyder-Poisson Algebra. UNIVERSE, v. 11, n. 10, p. 15-pg., 2025-10-14. (24/23831-0, 24/04134-6)