General (Noncommutative) Supersymplectic Mechanics: A Unified Symplectic View of Physics
Prof. Tulsi Dass
Chennai Mathematical Institute.
Employing a simple generalization of Dubois Violette's scheme of derivation- based noncommutative geometry, a general formalism of(super-) symplectic mechanics is developed which has, as special cases, classical and quantum Hamiltonian mechanics (of particles, fields and more general systems) and their super (i.e. $Z_2$-graded) versions. It permits a transparent treatment of quantum - classical correspondence and provides an attractive framework for the development of a fundamental theory in which one can adopt a quantum outlook from the beginning (in particular, there is a natural place for commutative superselection rules in the formalism), need not have space-time as a manifold at the basic level and for examining its implications at various levels.