Noncommutative version of an arbitrary nondegenerated mechanics
| dc.creator | Deriglazov, A. A. | |
| dc.date | 2002-08-10 | |
| dc.date.accessioned | 2026-07-07T04:13:58Z | |
| dc.date.available | 2026-07-07T04:13:58Z | |
| dc.description | A procedure to obtain noncommutative version for any nondegenerated dynamical system is proposed and discussed. The procedure is as follow. Let $S=\int dt L(q^A, ~ \dot q^A)$ is action of some nondegenerated system, and $L_1(q^A, ~ \dot q^A, ~ v_A)$ is the corresponding first order Lagrangian. Then the corresponding noncommutative version is $S_N=\int dt[ L_1(q^A, ~ \dot q^A, \~ v_A)+ \dot v_Aθ^{AB}v_B]$. Namely, the system $S_N$ has the following properties: 1) It has the same number of physical degrees of freedom as the initial system $S$. 2) Equations of motion of the system are the same as for the initial system $S$, modulo the term which is proportional to the parameter $θ^{AB}$. 3) Configuration space variables have the noncommutative brackets: $\{q^A, ~ q^B\}=-2θ^{AB}$. It is pointed also that quantization of the system $S_N$ leads to quantum mechanics with ordinary product replaced by the Moyal product. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/0208072 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0208072 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/51458 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Noncommutative version of an arbitrary nondegenerated mechanics | |
| dc.type | text |