Sesión Geometría y Teoría de LieNoncommutative spacetimes and spaces of geodesics from Poincaré and (A)dS Poisson-Lie groups
Iván Gutiérrez Sagredo
Universidad de Burgos, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
The theory of Poisson--Lie groups and Poisson homogeneous spaces [1,2] has applications in a wide range of different fields. In particular, in recent years, it has been applied to the construction of phenomenological models in quantum gravity [3]. Those models arise as the semiclassical approximation of fully noncommutative spacetimes covariant under quantum group symmetries.
In this talk, after motivating the physical interest of those models, I will present their systematic construction and how they allow to greatly extend their analysis. In particular, I will describe two important results based on coisotropic Poisson homogeneous spaces: firstly, the construction of noncommutative spaces of geodesics of maximally symmetric spacetimes of constant curvature [4,5,6,7]; secondly the extension of noncommutative spacetimes and noncommutative spaces of geodesics to the case of a non-vanishing cosmological constant [8,9]. In order to do this, I will describe Poisson--Lie structures on the Poincaré and (A)dS groups and the classical construction as coset spaces of the corresponding spacetimes and spaces of geodesics. Time permitting I will show how certain Poisson--Lie structures allow for the construction of all these spaces (including the spaces of time-, light- and space-like geodesics) while for others only some of them are possible [10].
Referencias
[1] V G Drinfel’d. 1987 Quantum groups Proc. Int. Congr. Math. (Berkeley 1986) 798–820.
[2] J Lu. Multiplicative and affine Poisson structures on Lie groups. PhD Thesis (1990).
[3] A Addazi et al. Quantum gravity phenomenology at the dawn of the multi-messenger era-a review. Progress in Particle and Nuclear Physics 125 (2022) 103948.
[4] A Ballesteros, I Gutierrez-Sagredo, FJ Herranz. Noncommutative spaces of worldlines. Physics Letters B 792 (2019) 175-181.
[5] A Ballesteros, G Gubitosi, I Gutierrez-Sagredo, F Mercati. Fuzzy worldlines with k-Poincaré symmetries. Journal of High Energy Physics 2021 (2021) 1-30.
[6] A Ballesteros, I Gutierrez-Sagredo, FJ Herranz. The noncommutative space of light-like worldlines. Physics Letters B 829 (2022) 137120.
[7] A Ballesteros, G Gubitosi, I Gutierrez-Sagredo, FJ Herranz. $\kappa$-Galilean and k-Carrollian noncommutative spaces of worldlines. Physics Letters B 838 (2023) 137735.
[8] A Ballesteros, I Gutierrez-Sagredo, FJ Herranz. The k-(A) dS noncommutative spacetime. Physics Letters B 796 (2019) 93-101.
[9] A Ballesteros, I Gutierrez-Sagredo, FJ Herranz. Noncommutative (A) dS and Minkowski spacetimes from quantum Lorentz subgroups. Classical and Quantum Gravity 39 (2021) 015018.
[10] A Ballesteros, I Gutierrez-Sagredo, FJ Herranz. All noncommutative spaces of k-Poincar\é geodesics. Journal of Physics A: Mathematical and Theoretical 55 (2022) 435205.