# The topological AC effect on non-commutative phase space

@article{Li2006TheTA, title={The topological AC effect on non-commutative phase space}, author={Kang Li and Jian-hua Wang}, journal={The European Physical Journal C}, year={2006}, volume={50}, pages={1007-1011} }

The Aharonov–Casher (AC) effect in non-commutative (NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp’s shift method. After solving the Dirac equations both on non-commutative space and non-commutative phase space by the new method, we obtain corrections to the AC phase on NC space and NC phase space, respectively.

## 86 Citations

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## References

SHOWING 1-10 OF 37 REFERENCES

### Non-commutative quantum mechanics and the Aharonov-Casher effect

- Physics
- 2004

Abstract.In this work a new method is developed to investigate the Aharonov-Casher effect in a non-commutative space. It is shown that the holonomy receives non-trivial kinematical corrections.

### Representations of non-commutative quantum mechanics and symmetries

- Physics, Mathematics
- 2003

Abstract.We present a unified approach to representations of quantum mechanics on non-commutative spaces with general constant commutators of the phase-space variables. We find two phases and duality…

### REPRESENTATION OF NONCOMMUTATIVE PHASE SPACE

- Mathematics
- 2005

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension.…

### Testing spatial noncommutativity via the Aharonov-Bohm effect

- Physics
- 2002

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives nontrivial kinematical corrections…

### Exact equivalence of spin-1/2 Aharonov-Bohm and Aharonov-Casher effects.

- PhysicsPhysical review letters
- 1990

It is shown that there is an exact equivalence between the Aharonov-Bohm effect for spin-1/2 particles and the Ah Sharonov-Casher effect, independent of whether relativistic or nonrelativistic kinematics are used.

### Hall effect in noncommutative coordinates

- Physics
- 2001

We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained.…