Hamiltonian formulation of generalized quantum dynamics: Quantum mechanical problem (Q1368213)

This paper is meant as a first into a series dedicated to a new formulation of quantum mechanics, first suggested by \textit{S. L. Adler} in `Quaternionic Quantum Mechanics and Quantum Fields', Oxford Univ. Press (1995). Using the total trace functional of an operator, the authors define two kinds of Poisson bracket: one called total trace Poisson bracket which gives the equation of motion of a total trace functional and another one called without-total-trace Poisson bracket which gives the equation of motion of an operator. Particulary, the Euler-Lagrange and Hamilton equations are obtained. These equations are quite similar in form to the corresponding equations in classical mechanics.