Compactness and Symmetry in Quantum Logic

A particularly simple and flexible mathematical framework for the study of probability theory classical, quantum and otherwise is the notion of a test space, i.e., a collection of (possibly overlapping) discrete sample spaces (as developed in the 1970s and 80s by D. J. Foulis, C. H. Randall and others). “Quantum logics” arise quite naturally as invariants of test spaces; however, the latter are much easier both to interpret and to manipulate. After providing a tutorial on test spaces, I’ll outline how this framework can usefully be enriched by the addition of topological and covariant structure. In particular, I’ll discuss topological test spaces that are highly symmetrical under the action of a compact group