Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the quantized space and its wavefunctions. It is shown that the motion of the particle in the field direction in time reversal invariant and rotationally invariant noncommutative space is the same as in the ordinary space (space with the ordinary commutation relations for operators of coordinates and operators of momenta). Noncommutativity of coordinates has influence only on the motion of the particle in the directions perpendicular to the field direction. Namely, space quantization has effect on the mass of the particle.
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 …
We consider a system of two particles in noncommutative space which is rotationally invariant. It is shown that the coordinates of the center-of-mass position and the coordinates of relative motion satisfy noncommutative algebra with corresponding effective tensors of noncommutativity. The hydrogen atom is studied as a two-particle system. We find the corrections to the energy levels of the hydrogen atom up to the second order over the parameter of noncommutativity.
We study disordered topological insulators with time reversal symmetry. Relying on the noncommutative index theorem which relates the Chern number to the projection onto the Fermi sea and the magnetic flux operator, we give a precise definition of the $Z_2$ index which is a noncommutative analogue of the Atiyah-Singer $Z_2$ index. We prove that the noncommutative $Z_2$ index is robust against any time-reversal symmetric perturbation including disorder potentials as long as the spectral gap at the Fermi level does not close.
We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform 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 gravitational filed is determined by its mass. The trajectory of motion of a particle in uniform gravitational field corresponds to the trajectory of harmonic oscillator with frequency determined by the value of parameter of momentum noncommutativity and mass of…
We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the $κ$-deformed space-time as a prototype. Upto the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to b…
In this paper, we consider the evaluation of the effective action for photons coupled to charged scalar fields in the framework of a $(2+1)$-dimensional noncommutative spacetime. In order to determine the noncommutative Maxwell Lagrangian density, we follow a perturbative approach, by integrating out the charged scalar fields, to compute the respective graphs for the vev's $\left\langle AA \right\rangle$, $\left\langle AAA \right\rangle$ and $\left\langle AAAA \right\rangle$. Surprisingly, it is shown that these contributions are planar and that, in the highly noncommutative limit, correspond …
Coulomb interactions famously drive three dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work, Phys. Rev. B 95, 205106 (2017), the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the bandstructure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder, and that a runaway flow to strong disorder occurs. In th…
