Stat. Field Theory Course

Mathematical Methods of Quantum Mechanics

CONTENTS

From Weyl systems to the Euclidean field theory, through the Feynman-Kac construction

COURSE LIVE JOURNAL

Nov, 16th: formalism of Classical vs Quantum Mechanics; observables, states, dynamics; canonical commutation relations and their nonunique realization; the Weyl system; Weyl algebra
Nov, 18th: C* algebras; the C* algebra of bounded operators on a Hilbert space; the GNS representation theorem; the uniqueness theorem of representation of the Weyl algebra
Nov, 23rd: setting of the problem for an infinite number of degrees of freedom, and related difficulties; Gaussian measures; the Fock representation
Nov, 28th: second quantization as a functor, uniqueness of the Weyl representation preserving strict positivity, Wiener process
Dec, 7th: the Schrödinger picture: Schrödinger equation; domains and the problem of the selfadjointness of the Hamiltonian; Lie-Trotter formula; Feynmann-Kac formula
Jan, 11th:
Jan, 13th:
Jan, 18th:
Jan, 20th:

SUGGESTIONS FOR THE SEMINAR-EXAM