Lectures on the mathematics of quantum mechanics I / Gianfausto Dell'Antonio.

Springer eBooks

Elements of the history of Quantum Mechanics I -- Elements of the history of Quantum Mechanics II -- Axioms, states, observables, measurement, di?culties -- Entanglement, decoherence, Bell’s inequalities, alternative theories -- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity and generators -- Operators on Hilbert spaces I; Basic elements -- Quadratic forms -- Properties of free motion, Anholonomy, Geometric phase -- Elements of C ?-algebras, GNS representation, automorphisms and dynamical systems -- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form -- Semigroups and dissipations. Markov approximation -- Quantum dynamical semigroups I -- Positivity preserving contraction semigroups on C ?-algebras -- Conditional expectations -- Complete Dissipations -- Weyl system, Weyl algebra, lifting symplectic maps --  Magnetic Weyl algebra -- A Theorem of Segal -- Representations of Bargmann, Segal, Fock -- Second quantization -- Other quantizations (deformation, geometric).

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