Lagrangian quantum theory. III. Coordinate-free formulation

Abstract

For pt.II, see abstr. A66629 of 1973. The authors show that the Frechet derivative, which they have previously used to formulate a quantum-mechanical version of Hamilton's principle of stationary action, suffers from certain defects. They set up a simpler, coordinate-free, formulation of quantum mechanics based on the Lie algebra of symmetric contravariant tensor fields on the configuration manifold of the system and re-express the principle of stationary action using this formalism. They find the same relation between Hamiltonian and Lagrangian as before, but a much larger class of allowable variations, namely those associated with and Cinfinity vector fields.