Speaker
Description
Physical systems in a noncommutative space with preserved time-reversal and rotational symmetries
Khrystyna Gnatenko
Professor Ivan Vakarchuk Department for Theoretical Physics, Ivan Franko National University of Lviv, 12, Drahomanov St., Lviv, 79005, Ukraine.
We consider a space with noncommutativity of coordinates and momenta with preserved time-reversal and rotational symmetries [1]. The noncommutative algebra is constructed by generalizing the parameters of coordinate and momentum noncommutativity to tensors, defined with the help of additional coordinates and momenta. They are governed by a rotationally invariant system. The resulting algebra is equivalent to a canonical-type noncommutative algebra and does not violate rotational or time-reversal symmetries [1].
We examine one- and many-particle systems in this space, including free particles, systems of harmonic oscillators, and exotic atoms. We derive corrections to the energy levels of these systems caused by space quantization [2]. Additionally, we discuss the problem of describing the motion of a macroscopic body in such a space. We propose conditions on the parameters of the noncommutative algebra that provide a resolution to the soccer-ball problem in noncommutative space.
Motion of a particle and a macroscopic body in gravitational field is examined in the noncommutative phase space. The problem of the violation of the weak equivalence principle is discussed [3,4]. On the basis of comparison of the results of theoretical studies with the experimental ones the upper bound on the minimal length and the minimal momentum are found [1].
[1] Kh. P. Gnatenko Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
Eur. Phys. J. Plus 135(8), 652 [12 p.] (2020)
[2] Kh. P. Gnatenko System of interacting harmonic oscillators in rotationally invariant noncommutative phase space Phys. Lett. A 382(46), 3317 (2018)
[3] Kh. P. Gnatenko, M. I. Samar, V. M. Tkachuk, Kepler problem in quantized space. Lviv: Lviv University Press, 2024. 136 pages.
[4] Kh. P. Gnatenko, V. M. Tkachuk Deformed Heisenberg algebras of different types with preserved weak equivalence principle J. Phys. Stud. 27(1), 1001 [19 p.] (2023)
