Category Theory in Physics  

In General > s.a. functors; logic; Structural Realism.
* Idea (Coecke): A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof.
* Examples of applications: Unitary representations of the Lorentz group [@ Crane gq/00]; > s.a. Topos Theory.
@ Reviews and introductions: Moore IJTP(98); Coecke in(06)-a0808, Coecke & Paquette a0905; Baez & Lauda in(11)-a0908 [n-categories].
@ General references: Thomas m.AG/00-proc; Marcinek m.QA/00 [particle interactions]; Oeckl JGP(03)ht/01 [generalized lattice gauge theory]; Coecke & Lal FP(12)-a1107 [causal structures and symmetric monoidal categories]; Lal & Teh a1404 [and physical structuralism]; Tull a1602 [operational theories of physics]; Amorim & Ben-Bassat a1601 [2 -category of Lagrangians].
@ Stacks: Sharpe ht/06-proc [and derived categories]; Benini et al a1704 [stack of Yang-Mills fields on Lorentzian manifolds].

In Gravitation
@ Classical gravity: Morava mp/04-conf [2-categories and topological gravity].
@ Quantum gravity / spacetime structure: Miković & Vojinović CQG(12) [and Poincaré 2-group]; & Ko Sanders; > s.a. modified approaches to quantum gravity; quantum spacetime models.

In Other Field Theories > s.a. fiber bundles [natural bundles]; types of yang-mills theories [based on Lie 2-groups].
@ References: Weatherall a1505 [rev, theoretical structure and theoretical equivalence]; Scholz a1607 [Weyl and automorphisms].

In Quantum Theory > s.a. generalized quantum mechanics.
@ General references: Schlesinger JMP(99); Abramsky & Coecke a0808-ch; Harding IJTP(09); Filk & von Müller AdP(10)-a0907 [framework]; Coecke & Perdrix a1004-proc [environment and classical channels]; Bergholm & Biamonte JPA(11)-a1010 [and quantum information science]; Abramsky & Heunen a1011 [H*-algebras and non-unital Frobenius algebras]; Lehmann a1012; Heunen FP(12) [complementarity]; Gogioso & Zeng a1501/ACS [representation theory]; Gogioso a1501, Bolotin a1502 [categorical semantics]; Heunen & Tull EPTCS(15)-a1506 [categories of relations as models]; Coecke & Kissinger a1510, a1605 [overview, 2/3].
@ Categorical quantum mechanics: Abramsky & Heunen a1206 [and operational theories]; Gogioso & Genovese EPTCS(17)-a1605 [infinite-dimensional], a1703 [Star Hilb].
@ n-categories: Kapustin a1004-proc [and topological field theory]; Vicary a1207 [2-categorical formalism for classical information, quantum systems, and their interactions].
@ Specific types of theories: Morton TAC(06)m.QA [combinatorial model for harmonic oscillator]; Coecke & Edwards a0808-proc [Spekkens' toy theory]; Stirling & Wu a0909 [braided systems].
> Specific topics: see fock space; particle models; particle statistics; quantum information [and 2-categories]; quantum oscillators; spin-statistics theorem.

In Other Disciplines
@ References: Hines a1303-in [categorical linguistics and models of meaning].

"If categories start showing up in your field, you should have left the field five years ago."
– Writing on the wall in one of the men's rooms at Perimeter Institute, 2002–2004.


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