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.

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.