We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.
We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations [x i , x j ] = iθ ij . Comparison with observation places severe constraints on the value of the noncommutativity parameter.
In this work a new method is developed to investigate the Aharonov-Casher effect in a noncommutative space. It is shown that the holonomy receives non-trivial kinematical corrections.
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