Lorentz transformations as Lie–Poisson symmetries
Copyright policy )Lorentz transformations as Lie–Poisson symmetries
We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson–Lie group. In so doing we obtain the classical limit of a particle moving on a noncommutative space possessing SLq(2, C) invariance. We show that if the standard mass shell constraint is chosen for the Hamiltonian function, then the particle interacts with the space–time. We solve for the particle trajectory and find that it originates and terminates at singularities.
- Biblioteca universitaria di Napoli Italy
- Alabama Agricultural and Mechanical University United States
- University Federico II of Naples Italy
High Energy Physics - Theory, FOS: Physical sciences, Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics, Hamiltonian function, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, mass shell constraint, particle trajectory, FOS: Mathematics, invariance, Quantum Algebra (math.QA), noncommutative space, classical limit
High Energy Physics - Theory, FOS: Physical sciences, Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics, Hamiltonian function, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, mass shell constraint, particle trajectory, FOS: Mathematics, invariance, Quantum Algebra (math.QA), noncommutative space, classical limit
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