Category Theory in Physics| 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];
Beer et al a1811 [applications in physics, anyons].
@ 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];
Amorim & Ben-Bassat ATMP(17)-a1601 [2 -category of Lagrangians];
Tull a1602 [operational theories of physics];
Veilahti a1712 [higher theory].
@ Stacks: Sharpe ht/06-proc [and derived categories];
Benini et al CMP(18)-a1704 [stack of Yang-Mills fields on Lorentzian manifolds];
Berktav a1907
[stacky formulation of general relativity, stack of Ricci-flat 3D Lorentzian metrics].
In Gravitation
@ Classical gravity: Morava mp/04-conf [2-categories and topological gravity];
Zuo a2007
[general relativity with a cosmological constant].
@ 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].
@ References: Weatherall a1505-in [rev, theoretical structure and theoretical equivalence];
Scholz a1607 [Weyl and automorphisms];
Tachikawa a1712-proc.
> Specific proposals: see theories
beyond the standard model; types of gauge theories and
yang-mills theories [based on Lie 2-groups].
In Quantum Theory > s.a. generalized quantum
mechanics; Topos Theory [Butterfield-Isham-Döring].
@ 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];
Coecke & Kissinger a1510,
a1605 [overview, 2/3];
Gogioso & Genovese EPTCS(18)-a1703 [quantum field theory];
Tull a1902-PhD [general operational theories];
de Ronde & Massri a2002 [pure and mixed states];
Gogioso a1905 [diagrammatic approach];
Heunen & Vicary 19.
@ Categories of relations:
Heunen & Tull EPTCS(15)-a1506 [as models];
Mehta & Zhang LMP(20)-a1907 [Frobenius objects].
@ Categorical quantum mechanics: Abramsky & Heunen a1206 [and operational theories];
Gogioso & Genovese EPTCS(17)-a1605 [infinite-dimensional],
EPTCS(18)-a1703 [*Hilb];
Gogioso a1709-PhD [dynamics];
Gogioso & Genovese a1805 [and quantum field theory].
@ n-categories: Kapustin a1004-proc [and topological field theory];
Vicary a1207
[2-categorical formalism for classical information, quantum systems, and their interactions];
Benini et al a2003 [2-categorical algebraic quantum field theories].
@ 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];
de Ronde & Massri IJTP(18)-a1801,
a1802,
a1807 [logos categorical approach].
> 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];
Blass & Gurevich BEATCS-a1807 [computer science].
"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.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 12 sep 2020