A PHASE-SPACE FORMULATION OF QUANTUM STATE FUNCTIONS

Allowing for virtual paths in phase space permits an extension of Hami lton's principle of least action, of lagrangians and of hamiltonians t o phase space. A subsequent canonical quantization, then, provides a f ramework for quantum statistical mechanics. The classical statistical mechanics and the conventional quantum mechanics emerge as special cas e of this formalism. Von Neumann's density matrix may be inferred from it. Wigner's functions and their evolution equation may also be obtai ned by a unitary transformation.