A Prehistory of n-Categorical Physics

Abstract

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks, string theory, loop quantum gravity, and topological quantum field theory. Our chronology ends around 2000, with just a taste of later developments such as open-closed topological string theory, the categorification of quantum groups, Khovanov homology, and Lurie's work on the classification of topological quantum field theories.

129 pages, 8 eps figures

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• Quantum GestART: Identifying and Applying Correlations between Mathematics, Art, and Perceptual Organization
• A 2-categorical state sum model
• Tensor Network Methods for Invariant Theory
• 2-Group Representations for Spin Foams
• Charged String Tensor Networks
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• The Abstract Structure of Quantum Algorithms
• Semi-entwining structures and their applications
• Proof Diagrams for Multiplicative Linear Logic
• Topological Quantum Field Theory via Chren-Simons Theory, part 1