## What is/are Noncommutative Phase?

Noncommutative Phase - In the present contribution, the Hirota-Satsuma coupled KdV hierarchy on noncommutative phase-space is investigated using the noncommutative extension of Lax pair generating technique.^{[1]}Additionally, a putative metric structure for the noncommutative phase-space is discussed.

^{[2]}In the rotationally invariant noncommutative phase space harmonic oscillator chain is studied.

^{[3]}We propose the way to recover the time reversal and rotational symmetries in noncommutative phase space of canonical type.

^{[4]}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.

^{[5]}These are indeed technically related to compactness of corresponding symplectic manifold in Snyder noncommutative phase space.

^{[6]}We find stringent upper bound on the momentum scale in noncommutative phase space of canonical type on the basis of studies of perihelion shift of the Mercury planet with taking into account features of description of motion of macroscopic body in the space with noncommutativity of coordinates and noncommutativity of momenta.

^{[7]}Noncommutative phase-space and its effects have been studied in different settings in physics, in order to unveil a better understanding of phase-space structures.

^{[8]}

## Invariant Noncommutative Phase

In the rotationally invariant noncommutative phase space harmonic oscillator chain is studied.^{[1]}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.

^{[2]}

## noncommutative phase space

In the rotationally invariant noncommutative phase space harmonic oscillator chain is studied.^{[1]}We propose the way to recover the time reversal and rotational symmetries in noncommutative phase space of canonical type.

^{[2]}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.

^{[3]}These are indeed technically related to compactness of corresponding symplectic manifold in Snyder noncommutative phase space.

^{[4]}We find stringent upper bound on the momentum scale in noncommutative phase space of canonical type on the basis of studies of perihelion shift of the Mercury planet with taking into account features of description of motion of macroscopic body in the space with noncommutativity of coordinates and noncommutativity of momenta.

^{[5]}