A Variational Formulation of Symplectic Noncommutative Mechanics

Abstract

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [14]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

17 pages, Latex. Accepted for publication in IJGMMP

References in corpus (8)

• Quantum mechanics on the noncommutative plane and sphere
• Noncommutative Geometry and Gravity
• The exotic Galilei group and the "Peierls substitution"
• Non-commutative space-time of Doubly Special Relativity theories
• Loop quantum gravity: an outside view
• Feynman problem in the noncommutative case
• Equations of motion, Noncommutativity and Quantization
• Classical and Quantum Systems: Alternative Hamiltonian Descriptions

Cited by in corpus (5)

• Electrodynamics on $\kappa$-Minkowski space-time
• Geodesic equation in $k$-Minkowski spacetime
• A Tail of a Quark in N=4 SYM
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Maxwell's equations and Lorentz force in doubly special relativity