Classical and Quantum Phase Space Mechanics

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.

List of contents

1. Introduction; 2. Elements of differential geometry; 3. Symplectic geometry and phase space mechanics; 4. Probability and statistical phase space mechanics; 5. Dissipation and contact phase space mechanics; 6. Quasi-probability and quantum phase space mechanics; 7. Decoherence and open quantum phase space mechanics; 8. Representation and possibility; References.

Product details

• Authors: Karim Pierre Yves (University of Bristol Thebault, Karim Pierre Yves Thébault
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Release: 31.12.2025
• EAN: 9781009352031
• ISBN: 978-1-0-0935203-1
• No. of pages: 75
• Series: Elements in the Philosophy of Physics
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; PHILOSOPHY / General, Philosophy: metaphysics & ontology, Philosophy: metaphysics and ontology, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Elementary Mechanics