Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries

TL;DR

This paper investigates the effects of rotationally and time-reversal invariant noncommutative phase space on planetary orbits, deriving bounds on noncommutativity parameters from Mercury's perihelion precession, and finds these bounds are significantly tighter than previous estimates.

Contribution

It introduces a rotationally and time-reversal invariant noncommutative algebra and derives bounds on momentum noncommutativity from planetary orbit data.

Findings

Upper bounds on noncommutativity parameters are established.

The bounds are at least ten orders lower than those from hydrogen atom studies.

Provides stringent restrictions on minimal momentum in noncommutative phase space.

Abstract

Noncommutative algebra which is rotationally invariant, time reversal invariant and equivalent to noncommutative algebra of canonical type is considered. Perihelion shift of orbit of a particle in Coulomb potential in the rotationally-invariant noncommutative phase space is found up to the second order in the parameters of noncommutativity. Applying the result to the case of Mercury planet and using observable results for precession of its orbit we find upper bounds on the parameters of noncommutativity in the rotationally-invariant noncommutative phase space. The obtained upper bound for the parameter of momentum noncommutativity is at least ten orders less than the upper bounds estimated on the basis of studies of the hydrogen atom in noncommutative phase space. As a result we obtain stringent restriction on for the minimal momentum in noncommutative phase space with preserved rotational and time reversal symmetries.