About the Project
This site and the book are under development. Lessons and exercises will be added gradually.
Planned content: Part I, isolated systems: mathematical formalism (mathematical physics), postulates, basic applications. Part II, interacting systems: entanglement, decoherence, measurement theory. Part III: interpretations of quantum mechanics and alternative theories. Part IV: quantum information, quantum algorithms. Part V: quantum gravity.
About This Book
Warning: this book is primarily written in French; the English version is automatically translated using Claude Sonnet 4.6.
This book proposes a rigorous formalization of modern quantum mechanics. Going beyond the scope of conventional introductory textbooks, it develops the essential tools of mathematical physics, from Hilbert spaces to advanced spectral theory, including topology and geometry.
This treatise is intended for readers who seek, beyond computational practice, to understand the logical necessity and foundation of the structures in use. The text addresses interpretational issues directly, with a detailed analysis of the measurement problem and decoherence, while also presenting alternative theories and their experimental constraints.
Intended for master's students, doctoral students, and researchers, it aims at a comprehensive command of the theory, uniting technical rigor with conceptual depth.
The text develops quantum mechanics from first principles, assuming a strong background in classical mechanics, electrodynamics, and mathematics. Proofs are given in full whenever they clarify the physics, and many worked examples complement the theoretical exposition.
Book Details
About the Author
Jean-Philippe Bruneton is a physicist at Université Paris Cité, France. His research interests include the laws of gravitation, quantum mechanics and its foundations, and symbolic regression as a machine learning task. This book grew from lecture notes developed over many years of teaching at graduate and advanced undergraduate level.
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