Topological (Quantum) Field Theories| Topological (Quantum) Field Theories |
In General > s.a. category [n-categories];
path-integral quantum field theory.
* Idea: (Quantum) field
theories in which correlators depend only on the topology of the manifold.
* Motivation: They generate
global smooth invariants for the manifold.
* Applications: Chern-Simons
theories have found application in the description of some exotic strongly-correlated
electron systems and the corresponding concept of topological quantum computing,
and topological sigma models describe digital memcomputing machines DMMs for
computing with instantons.
@ General references: Ivanenko & Sardanashvili MUPB(79);
Witten CMP(88);
Baulieu PLB(89);
Horne NPB(89);
Myers & Periwal PLB(89);
in Atiyah 90;
Rajeev PRD(90);
Birmingham et al PRP(91);
Wu CMP(91);
Roca RNC(93);
Anselmi CQG(97) [invariants];
Becchi et al PLB(97) [gauge dependence];
Vafa ht/00-conf;
Jones BAMS(09) [development, and subfactor theory];
Boi IJGMP(09);
Hellmann PhD-a1102
[and state sums on triangulated manifolds].
@ Books and reviews: Kaku 91;
in Nash 91;
Fré & Soriani 95;
Labastida ht/95-conf;
Labastida & Lozano ht/97-ln;
Kaul ht/99;
Schwarz ht/00;
Labastida ht/01-talk;
Kaul et al ht/05-en
[Schwarz-type, including Chern-Simons and BF];
Labastida & Mariño 05;
Ivancevic & Ivancevic a0810-ln;
Qiu a1201-ln;
Carqueville & Runkel a1705-ln.
@ Action:
Labastida & Pernici PLB(88);
Dayi NPB(90).
@ Observables: Labastida CMP(89);
Ouvry & Thompson NPB(90).
@ Algebraic / geometric structure:
Crane & Frenkel JMP(94);
Crane & Yetter pr(94).
@ BRST approach:
Birmingham et al NPB(89);
Chen PRD(90).
@ Applications: Di Ventra et al a1609 [DMMs and computing with instantons].
@ Related topics: Atiyah IHES(89) [axioms];
Birmingham et al NPB(90) [renormalization];
Gegenberg & Kunstatter AP(94) [partition function];
Kauffman & Lomonaco SPIE(06)qp,
qp/06 [q-deformed spin network approach],
SPIE(07)-a0707-in [and quantum computation];
> s.a. stochastic quantization.
Specific Theories > s.a. chern-simons theory;
path-integral approach; yang-mills theories.
@ Electromagnetism as a topological field theory:
Rañada LMP(89),
JPA(92).
@ General relativity / quantum gravity from topological field theory:
Toon CQG(94)ht/93;
Barrett JMP(95)gq;
Mielke PRD(08),
GRG(08) [BRST quantization];
Gielen JPCS(11)-a1109 [with linear constraints];
Morales et al EPJC(16)-a1602 [from 5D CS theory];
> s.a. 3D quantum gravity [lqg].
@ Topological quantum mechanics:
Dunne et al PRD(90);
Skagerstam & Stern IJMPA(90) [2+1 dimensions];
Rogers NPPS(00)ht.
@ Topological gauge theory: Ouvry et al PLB(89) [supersymmetric, quantization];
Brooks & Lue JMP(96) [monopoles];
Losev et al NPB(98) [Gromov-Witten paradigm];
Boldo et al IJMPA(03)ht,
IJMPA(04)ht/03,
NPPS(04)ht [observables];
Leal & Pineda MPLA(08) [abelian, and Milnor's link invariant];
Chen IJGMP(13)-a0803 [conceptual, historical];
Escalante & López-Osio IJPAM(12)-a1203 [Euler and second-Chern classes, Hamiltonian analysis].
@ Topological gauge theory, deformed: Kondo PRD(98)ht;
García-Compeán & Paniagua GRG(05)ht/04 [non-commutative].
@ Topological (super)gravity:
Chamseddine NPB(90);
Koehler et al NPB(90);
> s.a. Topological Gravity.
@ Gravity and topological matter:
Gegenberg & Mann PRD(99)ht.
@ Homotopy quantum field theory:
Brightwell & Turner m.QA/01,
Brightwell et al IJMPA(03)m.AT/02;
Turaev 10;
Yau a1802 [monograph].
@ Other theories: Floreanini & Percacci MPLA(90) [pregeometry];
Gozzi & Reuter PLB(90) [classical mechanics as a topological field theory];
Birmingham et al IJMPA(90);
Blau & Thompson AP(91),
PLB(91) [forms];
Witten IJMPA(91) [cohomological];
Gamboa IJMPA(92);
Dijkgraaf & Moore CMP(97) [balanced];
Husain & Jaimungal PRD(99)ht/98 [holographic];
Adams & Prodanov LMP(00) [Schwarz's, Z];
Malik JPA(01)ht/00 [2D];
Ferrari mp/01 [simple cubic model];
Koroteev & Zayakin proc(07)ht/05 [example based on Morse theory];
Husain PRL(06)
[harmonic oscillator duals and background-independence in quantum gravity];
Mathews AHP(14)-a1201 [elementary, combinatorial theory];
> s.a. BF theory; m-theory.
Related Topics > s.a. 4D manifolds;
dynamical systems; spin networks [invariants].
@ On manifolds with boundary: Husain & Jaimungal PRD(99)ht/98;
Bel'kov et al a0907 [triangulated boundary];
Amoretti et al PRD(14)-a1410;
Corichi & Vukašinac IJMPD-a1809 [Hamiltonian analysis].
@ On lattices:
Wheater PLB(89) [Ising-like],
PLB(91) [gauge theories];
Bonzom & Smerlak LMP(10)-a1004 [degree of bubble divergences];
Bietenholz et al JHEP(10)-a1009 [actions].
@ (2+1)D theories and (3+1)D theories with defects: Dittrich JHEP(17)-a1701 [and and self-dual quantum geometries].
@ And knots / links: Horowitz & Srednicki CMP(90) [linking numbers];
Blanchet et al Top(95) [knot invariants];
Leal PRD(02);
Lemes et al PLB(99) [linking observables];
Labastida ht/00-conf,
ht/00-ln;
Leal & Pineda MPLA(08)-a0705 [topological field theory of Milnor's link invariant];
Sleptsov MPLA(14) [generalization, superpolynomial invariants of knots];
> s.a. knot invariants.
@ Other topics:
Eguchi MPLA(92) [and singularities];
Toon MPLA(94)ht/92 [particle content];
Archer JGP(95) [on PL manifolds];
Brooks & Lifschytz NPB(95)
[Donaldson topological invariants and quantum gravity];
Mukku et al JPA(97) [order-chaos];
Freedman et al CMP(02)qp/00 [and quantum computing];
Rovelli & Speziale GRG(07)
[expansion of field theories around a topological field theory];
Freed BAMS(13)-a1210 [extended topological quantum field theories and the cobordism hypothesis];
Carqueville a1607-proc
[2D with defects, functorial and algebraic description, intro].
> Phenomenology:
see cosmological-constant problem.
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