Alternative structures and bi-Hamiltonian systems

Abstract

In the study of bi-Hamiltonian systems (both classical and quantum) one\nstarts with a given dynamics and looks for all alternative Hamiltonian\ndescriptions it admits.In this paper we start with two compatible Hermitian\nstructures (the quantum analog of two compatible classical Poisson brackets)\nand look for all the dynamical systems which turn out to be bi-Hamiltonian with\nrespect to them.\n