Volume 123, Number 5, September 2018
|Number of page(s)||7|
|Published online||27 September 2018|
Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
Ivan Franko National University of Lviv, Department for Theoretical Physics - 12 Drahomanov St., Lviv, 79005, Ukraine and Laboratory for Statistical Physics of Complex Systems, Institute for Condensed Matter Physics, NAS of Ukraine 79011, Lviv, Ukraine
Received: 21 July 2018
Accepted: 3 September 2018
We study the influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and nonuniform gravitational fields in noncommutative phase space of canonical type with preserved rotational symmetry. It is shown that because of noncommutativity the motion of a particle in a gravitational field is determined by its mass. The trajectory of motion of a particle in a uniform gravitational field corresponds to the trajectory of a harmonic oscillator with frequency determined by the value of the parameter of momentum noncommutativity and mass of the particle. The equations of motion of a macroscopic body in a gravitational field depend on its mass and composition. From this follows a violation of the weak equivalence principle caused by noncommutativity. We conclude that the weak equivalence principle is recovered in rotationally invariant noncommutative phase space if we consider the tensors of noncommutativity to be dependent on mass. So, finally we construct noncommutative algebra which is rotationally invariant, equivalent to noncommutative algebra of canonical type, and does not lead to violation of the weak equivalence principle.
PACS: 03.65.-w – Quantum mechanics / 11.10.Nx – Noncommutative field theory
© EPLA, 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.