Mathematics

Web page: http://people.sissa.it/~alemiche/teaching2015-2016_QM-foundations.html

Web Page: http://people.sissa.it/~alemiche/teaching2015-2016_MQM.html

Web page: http://www.goliveira.org/courses/introduction-to-spectral-geometry-2016/

Topics:
- introduction to the theory of C*-algebras and von Neumann algebras
- representations
- automorphisms and dynamical systems
- KMS condition
- contraction semigroups
- algebraic formulation of Quantum Mechanics and Statistical Mechanics
- elements on the algebraic and the constructive Quantum Field Theory

Webpage:

http://people.sissa.it/~alemiche/teaching2016_Yajima.html

Topics:

• scratch course of spectral theory of operators on Hilbert spaces
• a reminder of classical probability
• fundamental postulates of quantum physics
• Heisenberg uncertainty principle
• the von Neumann-Lüders postulate, and the issue of individual states
• symmetries and the Wigner-Kadison theorem
• symmetry groups
• projective representations
• eliminability of multipliers for one parameter groups
• Weyl relations
• von Neumann uniqueness
• CCR and uncertainties