Stat. Field Theory Course
##
**Mathematical Methods of Quantum Mechanics **

###
Gianfausto Dell'Antonio

**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**

- math-ph/0510087 (Euclidean field theory)
- math-ph/0601029 (Gaussian transform of the Weil representation)
- Comm. Pure Appl. Math. 14 (1961) 187-214
- Cont. Math. 214 (1998), 47-62

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