др Марија Димитријевић Ћирић

31. марта 2021.

У оквиру семинара Групе за гравитацију, честице и поља Института за физику у Београду, у петак, 02. априла 2021. године у 11:15 путем BigBlueButton платформе, др Марија Димитријевић Ћирић (Физички факултет, Универзитет у Београду), одржаће предавање:

Application of L-infinity Algebras:
Braided Deformation of Field Theory and Noncommutative Gravity


In this talk we discuss a possibility to apply the L-infinity algebra formalism in construction of field theories and gravity on noncommutative spaces. To do this we have to introduce a new homotopy algebraic structure, that we call a braided $L_\infty$-algebra. Then we use the braided $L_\infty$-algebra to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act (in a standard/obvious way) on the solutions of the field equations.

In the first talk we will motivate the introduction of braided gauge field theories and we will repeat the basics of the twist deformation formalism introduced by Drinfeld in 1985.

In the second talk we will define braided gauge theories and discuss how they fit in the braided L-inifinity algebra formalism. Finally, we will present two examples: braided Chern-Simons theory and braided
Einstein-Cartan-Palatini 4D gravity.

The seminar is based on:

M. Dimitrijevic, Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo,
$L_\infty$-Algebras of
Einstein-Cartan-Palatini Gravity, JMP  61, 112502 (2020),  arXiv:

M.Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, {\it
Braided $L_\infty$-Algebras, Braided Field Theory and Noncommutative
Gravity}, arXiv:2103.08939.

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