Noncommutative version of an arbitrary nondegenerated mechanics

2002/08/10 by A. A. Deriglazov, Deriglazov, A. A.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0208072

5 pages

arxiv created 2002/08/10 · arxiv updated 2009/11/30

Abstract

A procedure to obtain noncommutative version for any nondegenerated dynamical system is proposed and discussed. The procedure is as follow. Let S=∫ dt L(q^A, ~ q^A) is action of some nondegenerated system, and L₁(q^A, ~ q^A, ~ v_A) is the corresponding first order Lagrangian. Then the corresponding noncommutative version is S_N=∫ dt[ L₁(q^A, ~ q^A, \~ v_A)+ v_Aθ^ABv_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.

Related

• Noncommutative quantum mechanics as a constrained system
• Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space
• Yang-Mills models on Noncommutative background
• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• Some Aspects of Noncommutativity on Real, p-Adic and Adelic Spaces