INVARIANT TORI AND HEISENBERG MATRIX-MECHANICS - A NEW WINDOW ON THE QUANTUM-CLASSICAL CORRESPONDENCE

Despite the seminal connection between classical multiply periodic mot ion and Heisenberg matrix mechanics, we show that there are fundamenta l, previously undisclosed aspects of this quantum-classical correspond ence. These include a quantum variational principle that implies the c lassical variational principle for invariant tori and the connection b etween commutation relations and quantization of action variables. Pos sible applications are described briefly.