Abstract
A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function \({\mathcal{H}}_{\mathrm{nc}}\) describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form ωnc is defined. A related NC Poisson bracket is obtained. This permits to construct the NC Hamiltonian vector field, also called NC geodesic flow. Further, using a canonical transformation induced by a generating function from the Hamilton–Jacobi equation, we obtain a relationship between old and new coordinates, and their conjugate momenta. These new coordinates are used to re-write the NC recursion operator in a simpler form, and to deduce the corresponding constants of motion. Finally, all obtained physical quantities are re-expressed and analyzed in the initial NC canonical coordinates.
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Hounkonnou, M.N., Landalidji, M.J., Baloїtcha, E. (2019). Recursion Operator in a Noncommutative Minkowski Phase Space. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVI. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01156-7_9
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DOI: https://doi.org/10.1007/978-3-030-01156-7_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-01155-0
Online ISBN: 978-3-030-01156-7
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