arXiv:1110.4492 · AIP conference proceedings

Information dynamics and new geometric foundations of quantum theory

Ryszard Paweł Kostecki

Published Jan 1, 2012• 1 citation

Abstract

We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by nonlinear geometry of spaces of integrals on abstract non-commutative algebras. New dynamics is defined by constrained maximisation of quantum relative entropy. We recover Hilbert space based approach (including unitary evolution and the von Neumann-Lüders rule) and measure theoretic approach to probability theory (including Bayes' rule) as special cases of our approach.

DOI: 10.1063/1.3688971

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