Foundations of Quantum Mechanics

Erhard Scheibe

Antonino Drago

I review the various algebraic foundations of quantum mechanics. They have been suggested since the birth of this theory till up to last year. They are the following ones: Heisenberg-Born-Jordan (1925), Weyl (1928), Dirac (1930), von Neumann (1936), Segal (1947), T.F. Jordan (1986), Morchio and Strocchi (2009) and Buchholz and Fregenhagen (2019). Three cases are stressed: 1) the misinterpretation of Dirac foundation; 2) von Neumann conversion from the analytic approach of Hilbert space to the algebraic approach of the rings of operators; 3) the recent foundation of quantum mechanics upon the algebra of perturbation Lagrangians. Moreover, historical considerations on the go-and-stop path performed by the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices till up to group theory and C*-algebras. But there was no progress in approaching closer the foundations of physics; therefore the problem of discovering an algebraic formulation of QM organized as a problem-based theory and making use of no more than constructive mathematics is open.

L. E. Ballentine

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.

Anshveer Bindra

Jaroslav Zamastil, Jakub Benda

Luigi Accardi

This conference was devoted to fundamental questions raised by quantum mechanics, especially in quantum information theory. As has become customary in our series of conference in Vaxjo, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the foundations of probability and physics. This conference belongs to the series of Vaxjo conferences in foundations of quantum mechanics (especially probabilistic foundations) combined of two subseries, Foundations of Probability and Physics: 2000, 02, 04, 06, 08, and Quantum Theory: Reconsideration of Foundations: 2001, 03, 05, 07. We also mention the first Vaxjo conference: Bohmian mechanics 2000. This is definitely the longest series of conferences on foundations in the history of quantum mechanics.