Introduction to and Historical Overview of Quantum Logics

          @misc{ scivideos_PIRSA:05070090,
            doi = {10.48660/05070090},
            url = {https://pirsa.org/05070090},
            author = {Wilce, Alexander},
            keywords = {},
            language = {en},
            title = {Introduction to and Historical Overview of Quantum Logics },
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2005},
            month = {jul},
            note = {PIRSA:05070090 see, \url{https://scivideos.org/index.php/pirsa/05070090}}
          }
          

Abstract

Introductory lecture summary: 1. Finite dimensional hilbert spaces and (complemented) modular lattices; infinite-dimensional hilbert spaces and orthomodularity. 2. von Neumann's QL; von Neumann-Birkhoff (briefly!); reconstruction of QM from P(H) 3. Mackey's programme; some early axiomatics (e.g., Zierler); QLs as OMPs + order-determining sets of states 4. Piron's Theorem; some discussion of Piron's axioms 5. Keller's examples (maybe just a mention, though I'd like to indicate how they come up); Soler's theorem (just the statement) 6. Abstract OMLs; Greechie Diagrams and the Loop Lemma; brief mention of Harding's results on decompositions 7. Tensor products (the F-R example, showing OMLs not stable under tensor products); orthoalgebras. 8. Orthoalgebras from test spaces