Tensor Coordinates in Noncommutative Mechanics

Abstract

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly used, and the object of noncommutativity ${\theta }^{ij}$ plays a fundamental rule as an independent quantity. The presented classical theory, as its quantum counterpart, is naturally invariant under the rotation group $SO(D)$.

12 pages, Latex

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Cited by in corpus (15)

• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Noncommutative relativistic particles
• Quantum complex scalar fields and noncommutativity
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Noncommutative Particles in Curved Spaces
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• The Strong Interaction Model in DFR noncommutative space-time
• From Noncommutative Sphere to Nonrelativistic Spin
• The standard electroweak model in the noncommutative $DFR$ space-time
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time