Springer-Verlag Berlin Heidelberg, 2011. — 1031 p. — (Lecture Notes in Physics 813). — ISBN: 978-3-642-12821-9 (eBook), 978-3-642-12820-2 (Softcover).This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity.These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures.Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.Contents: Introduction to Categories and Categorical Logic. Physics, Topology, Logic and Computation: A Rosetta Stone. Categories for the Practising Physicist. A Survey of Graphical Languages for Monoidal Categories. Geometry of Interaction and the Dynamics of Proof Reduction: A Tutorial. Dagger Categories and Formal Distributions. Proof Nets as Formal Feynman Diagrams. Compact Monoidal Categories from Linguistics to Physics. Domain Theory and Measurement. A Partial Order on Classical and Quantum States. Domain Theory and General Relativity. Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism. “What is a Thing?”: Topos Theory in the Foundations of Physics. Can a Quantum Computer Run the von Neumann Architecture?. A Categorical Presentation of Quantum Computation with Anyons.
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