Foundations of phase-space quantum mechanics

Karim P. Y. Thébault

This Element explores the formal and conceptual foundations of phase space formulations of classical and quantum mechanics. It provides an overview of the core mathematical and physical content of Hamiltonian mechanics, stochastic phase space mechanics, contact Hamiltonian mechanics, and open and closed quantum mechanics on phase space. The formal material is unified via three interpretative themes relating to structured possibility spaces, Liouville's theorem and its failure, and the classical and quantum notions of open and closed systems. This Element book is intended for researchers and graduate students in the philosophy and foundations of physics with an interest in the conceptual foundations of physical theory.

Nicolaas P. Landsman

Róbert Hermann

Several geometric remarks on the foundations of quantum mechanics are presented. For example, quantum phase space is the tangent bundle to quantum configuration space.

Manuel Gadella

Franklin E. Schroeck

David G. Long