Mathematical Foundations of Quantum Mechanics: An Advanced Short Course
Valter Moretti
TL;DR
This paper provides an advanced mathematical overview of quantum mechanics, focusing on its foundational structures like orthomodular lattices and C*-algebras, to deepen understanding of its theoretical underpinnings.
Contribution
It offers a comprehensive review and extension of the mathematical foundations of quantum mechanics, emphasizing lattice theory and algebraic formulations.
Findings
Clarifies the role of orthomodular lattices in quantum logic
Introduces the C*-algebraic approach to quantum theories
Connects mathematical structures with physical symmetries
Abstract
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C*-) algebraic formulation of quantum theories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.