TL;DR
This paper explicitly calculates the symplectic structure of SL(N,C), defines a Hamiltonian for free motion on SU(N), and solves the equations of motion, revealing a non-linear relation between velocity and momentum.
Contribution
It provides a detailed formulation of free motion on the Poisson SU(N) group, including explicit symplectic structure and equations of motion solutions.
Findings
Explicit symplectic structure of SL(N,C) derived
Hamiltonian for free motion on SU(N) formulated
Solutions to equations of motion obtained
Abstract
SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.
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