Fundamental Mathematical Structures of Quantum Theory

Prof. Valter Moretti is Full Professor of Mathematical Physics at the University of Trento (Italy). His research interests include rigorous quantum field theory in curved spacetime, mathematical aspects of quantum mechanics and general relativity, the applications of operator algebras, functional analysis and global analysis to quantum field theory, and mathematical (analytic and geometric) methods for physics.

“Moretti’s text is a fun and insightful tour through analytic aspects of quantum mechanics. In particular, it is an excellent resource for the spectral theory of unbounded operators. … This reviewer would find the text most useful as a supplement to a second course in functional analysis based on any of the more classic graduate texts. It is also well suited to self-study by graduate students/researchers transitioning to mathematical physics.” (Ryan Grady, MAA Reviews, January 6, 2023)“The book can be read on the basis of an elementary knowledge of Hilbert spaces and measure theory. For mathematicians, it can be used as an introduction to Quantum Mechanics and a detailed guide to the associated mathematical problems; for the reader familiar with Quantum Mechanics, it provides an extensive insight into the mathematical discussion of its structural and foundational issues.” (Giovanni Morchio, Mathematical Reviews, June, 2020)

• General Phenomenology of the Quantum World and Elementary Formalism.- Hilbert Spaces and Classes of Operators.- Observables and States in General Hilbert Spaces: Spectral Theory.- Fundamental Quantum Structures on Hilbert Spaces.- Realism, Non-Contextuality, Local Causality, Entanglement.- von Neumann Algebras of Observables and Superselection Rules.- Quantum Symmetries.- The Algebraic Formulation.