Mathematical Quantum Physics

This book provides the rigorous mathematical foundations of Quantum Physics, from the operational meaning of the measuring process to the most recent theories for the quantum scale of space-time geometry. Topics like relativistic invariance, quantum systems with finite and infinitely many degrees of freedom, second quantisation, scattering theory, are all presented through the formalism of Operator Algebras for a precise mathematical justification. The book is targeted to graduate students and researchers in the area of theoretical/mathematical physics who want to learn about the mathematical foundations of quantum physics, as well as the mathematics students and researchers in the area of operator algebras/functional analysis who want to dive into some of the applications of the theory to physics.

Aims to bridge the gap between physics and mathematics textbooks Gives an overview and a discussion of algebraic quantum field theory as it developed historically Provides a reference to the current state-of-the-art in local quantum physics

Auteur
Gabriele Nunzio Tornetta is a theoretical physicist who has worked on algebraic quantum field theory and the theory of classification of C-algebras. His research work included DFR models for non-commutative space-time and bivariant structures for the classification of nuclear C-algebras. He is also the author of publications in the area of machine learning. After his PhD in Pure Mathematics at the University of Glasgow, Dr Tornetta now works within the open-source software community, contributing to projects like CPython, among others.

Résumé
"The book is written in a nice style. It is meant for mathematicians with a knowledge of quantum mechanics or theoretical physicists with good skills in functional analysis." (Marek Nowakowski, Mathematical Reviews, October, 2023)

Contenu
The Basic Postulates.- Relativistic Invariance.- Quantum Mechanics.- Quantum Field Theory.- Further Topics.