Categories of Physical Processes [article]

Stanisław Szawiel
2017 arXiv   pre-print
We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor GNS : Phys⟶∗Mod, based on the Gelfand-Naimark-Segal construction and the notion of representability. We derive the probabilistic interpretation of quantum mechanics, including the Born rule, the Schrödinger and Heisenberg pictures, the relation between symmetries and group representations, and a theory of quantum Markov processes, including wave function collapse.
more » ... lusion of the classical limit and deformation quantization is briefly sketched. Gauge symmetry and extended locality cannot currently be accommodated, due to conceptual difficulties discussed in an appendix.
arXiv:1709.09096v2 fatcat:3zlwsidjevednbdavqbpaxmbwa