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.
Author(s): S. Abramsky, N. Tzevelekos (auth.), Bob Coecke (eds.)
Series: Lecture Notes in Physics 813
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 1031
Tags: Mathematical Methods in Physics;Category Theory, Homological Algebra;Theory of Computation
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Introduction to Categories and Categorical Logic....Pages 3-94
Physics, Topology, Logic and Computation: A Rosetta Stone....Pages 95-172
Categories for the Practising Physicist....Pages 173-286
Front Matter....Pages 287-287
A Survey of Graphical Languages for Monoidal Categories....Pages 289-355
Geometry of Interaction and the Dynamics of Proof Reduction: A Tutorial....Pages 357-417
Front Matter....Pages 419-419
Dagger Categories and Formal Distributions....Pages 421-436
Proof Nets as Formal Feynman Diagrams....Pages 437-466
Compact Monoidal Categories from Linguistics to Physics....Pages 467-487
Front Matter....Pages 489-489
Domain Theory and Measurement....Pages 491-591
A Partial Order on Classical and Quantum States....Pages 593-683
Front Matter....Pages 685-685
Domain Theory and General Relativity....Pages 687-703
Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism....Pages 705-752
“What is a Thing?”: Topos Theory in the Foundations of Physics....Pages 753-937
Front Matter....Pages 939-939
Can a Quantum Computer Run the von Neumann Architecture?....Pages 941-982
A Categorical Presentation of Quantum Computation with Anyons....Pages 983-1025
Back Matter....Pages 1027-1031
