MATH 666 Mathematical Foundations of Quantum Mechanics
Banach and Hilbert spaces, contraction mapping theorem, Lorentzian time delays, motion of n-charges in their electromagnetic field. Hamiltonian mechanics and category of Hamiltonian flows. Randomness due to initial trajectory. Direct integral of Hilbert spaces and probability amplitude. Description of position and momenta by self-adjoint operators. Functor of classical analogy. Heisenberg's and Schroedinger's representations. C*-algebras and operational calculus of operators based on Baire functions. Existence of spectral representations. Prerequisites: 624, 625, and 646.