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A variational formulation of symplectic noncommutative mechanics. (English) Zbl 1142.70007

Summary: 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 for 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. We hope that this variational formulation in configuration space can help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

MSC:

70G75 Variational methods for problems in mechanics
70H99 Hamiltonian and Lagrangian mechanics
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
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