Poisson Electrodynamics and Applications

• Grant number: 24/04134-6
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2024
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Vladislav Kupriyanov
• Grantee: Vladislav Kupriyanov
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Santo André , SP, Brazil
• City of the host institution: Santo André

Abstract

Constructing gauge theories on non-commutative spaces of general form is a notoriously difficult problem which attracts attention of theoretical physicists and mathematicians for more then two decades. Nevertheless, it is still not completely understood in full generality. Poisson electrodynamics is a semi-classical limit of non-commutative U(1) gauge theory. In recent years we have formulated three new approaches to consistent non-commutative and even non-associative deformations of gauge theory. The first one employs the framework of homotopy algebras and is a powerful tool for the construction of order by order non-commutative deformation. The second and the third approaches make use of the elements from the symplectic geometry and are better adapted for obtaining of the explicit all-order expressions as well as understanding of geometric nature of the obtained models. Several interesting results have been obtained and published in this direction. In this project we briefly describe the three approaches and formulate the topics of the future research, including the further development of the mathematical formalism and its application to the investigation of physical effects caused by the non-commutativity. (AU)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

BASILIO, B. S.; KUPRIYANOV, V. G.; KURKOV, M. A.. Charged particle in Lie-Poisson electrodynamics. EUROPEAN PHYSICAL JOURNAL C, v. 85, n. 2, p. 11-pg., 2025-02-12. (24/04134-6)

KUPRIYANOV, VLADISLAV; KURKOV, MAXIM; SHARAPOV, ALEXEY. Classical mechanics in noncommutative spaces: confinement and more. EUROPEAN PHYSICAL JOURNAL C, v. 84, n. 10, p. 13-pg., 2024-10-16. (24/04134-6)

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)