Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect
| Autor: | Gangopadhyay, Sunandan, Scholtz, Frederik G |
|---|---|
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 47 (2014) 075301 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/47/7/075301 |
| Popis: | The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field and an arbitrary potential. Using this action, the equation of motion and the ground state energy for the partcle are obtained explicitly. The Aharonov-Bohm phase is derived using a variety of methods and several dualities between this system and other commutative and noncommutative systems are demonstrated. Finally, the equivalence of the path integral formulation with the noncommutative Schr\"{o}dinger equation is also established. Comment: 12 pages Latex, References added, To appear in J.Phys.A |
| Databáze: | arXiv |
| Externí odkaz: |
|