Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
| dc.creator | Gitman, D. M. | |
| dc.creator | Kupriyanov, V. G. | |
| dc.date | 2007-07-02 | |
| dc.date | 2007-07-05 | |
| dc.date.accessioned | 2026-07-07T11:17:26Z | |
| dc.date.available | 2026-07-07T11:17:26Z | |
| dc.description | It is known that actions of field theories on a noncommutative space-time can be written as some modified (we call them $θ$-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and usual quantum mechanical features of the corresponding field theory. The $θ$-modification for arbitrary finite-dimensional nonrelativistic system was proposed by Deriglazov (2003). In the present article, we discuss the problem of constructing $θ$-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract $θ$-modified actions of the relativistic particles from path integral representations of the corresponding noncommtative field theory propagators. We consider Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as $θ$-modified actions of the relativistic particles. To confirm the interpretation, we quantize canonically these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The $θ$-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. | |
| dc.identifier | https://arxiv.org/abs/0707.0310 | |
| dc.identifier | http://arxiv.org/abs/0707.0310 | |
| dc.identifier | Eur.Phys.J.C54:325-332,2008 | |
| dc.identifier | doi:10.1140/epjc/s10052-007-0518-x | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/193008 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action | |
| dc.type | text |