On Thursday, January 16, we will have a LIRa session with Shengyang Zhong. Everyone is cordially invited!
Speaker: Shengyang Zhong (University of Amsterdam)
Title: Relational Structures in Quantum Logic
Date and Time: Thursday, January 16 2014, 15:30-17:30
Venue: Science Park 107, Room F1.15
This talk aims at investigating the role played by relational structures in the study of quantum logic. It will start with some background from quantum physics. Then a brief survey will follow about the traditional lattice-theoretic approach to quantum logic started by Birkhoff and von Neumann (1936). After this, we will proceed to the perspective from relational structures on quantum logic. Various relational structures will be discussed about, including orthoframes and orthomodular frames in Goldblatt (1974), state spaces in Moore (1995) and quantum dynamic frames in Baltag and Smets (2005). Their significance will be manifested by several representation theorems for different lattices in quantum logic. Then I will introduce a kind of relational structures called quantum Kripke frames proposed by myself. I will present the definition and explain how they relate to other structures in the study of quantum logic. The talk will end with some directions for future work, including axiomatization of quantum Kripke frames and probabilistic quantum Kripke frames.
No knowledge about quantum physics and its mathematical formalism is assumed, but familiarity with some basic notions from linear algebra will be helpful.
– Baltag, A. and Smets, S. (2005). Complete Axiomatizations for Quantum Actions. International Journal of Theoretical Physics, 44(12):2267-2282.
– Birkhoff, G. and von Neumann, J. (1936). The Logic of Quantum Mechanics. The Annals of Mathematics, 37:823-843.
– Goldblatt, R. (1974). Semantic Analysis of Orthologic. Journal of Philosophical Logic, 3:19-35.- Moore, D. (1995).Categories of Representations of Physical Systems.Helv Phys Acta, 68:658-678.