Observables and quantum spacetimes

Abstract: Noncommutative geometry, as the generalised notion of geometry, can be helpful in providing the phenomenological models quantifying the effects of quantum gravity. The noncommutative nature allows for obtaining quantum gravitational corrections to the classical solutions. One of the mostly studied possible phenomenological effects of quantum gravity is the modifications in wave dispersion.

In my talk I will introduce the mathematical framework for quantum spacetimes within the Hopf algebras and Drinfeld twists formalisms. Twisted differential calculus and twisting generators of the Hopf algebra symmetry allow on a fresh look on modifications in dispersion relations and offer a proper choice of physical observables as generators of the quantum Lie algebra of symmetries. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. The formalism also allows for study of the curved backgrounds. I will present recent results on propagation of waves in noncommutative cosmology and on the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime.

The talk will base on the results developed in collaboration with P. Aschieri and A. Borowiec [Observables and Dispersion Relations in k-Minkowski Spacetime J. High Energ. Phys. 2017, 152 (2017) arXiv:1703.08726, Dispersion Relations in κ-Noncommutative Cosmology arXiv:2009.01051].

astrophysicscondensed mattergeneral relativity and quantum cosmologyhigh energy physicsmathematical physicsclassical physicsgeneral physics

Audience: researchers in the topic

Theoretical physics seminar @ Tartu