Topology in Physics

In General
@ Topological quantum numbers, invariants: Thouless 98; Kellendonk & Richard mp/06-in [bulk vs boundary, and topological Levinson theorem]; > s.a. yang-mills gauge theory.
@ Reviews: Balachandran FP(94)ht/93; Nash in(98)ht/97; Lantsman mp/01.

In Minkowski Field Theory > s.a. electromagnetism; gauge theory; Susceptibility [topological].
* In gauge theory: The three paradigms of topological objects are the Nielsen-Olesen vortex of the abelian Higgs model, the 't Hooft-Polyakov monopole of the non-abelian Higgs model, and the instanton of Yang-Mills theory.
@ In gauge theory: Monastyrsky 93 [and condensed matter]; Gross JMP(96) [cohomology and connections]; Lenz ht/04, Jackiw ht/05-in [rev].
@ Related topics: Kiehn mp/01 [topology-changing evolution]; Díaz & Leal JMP(08) [invariants from field theories].

In Gravitation and Cosmology > s.a. Alexandrov Topology; geon; lorentzian and riemannian geometry; spacetime topology.
* Spacetime topology: The spacetime manifold can be assigned different topologies; The most natural ones are the manifold topology, the Alexandroff topology (generated by g_ab and the I ^+/–'s), and Johan's strong topology for compact spacetimes (more stable under limits).
* Spatial topology: Any compact 3-topology can occur classically, since it can be given a metric such that R = –k, with k a positive constant, and with this metric it can be made to satisfy the constraints, with K_ab = g_ab, for some constant .
@ References: Clarke GRG(71) [and general relativity]; Friedman & Mayer JMP(82) [angular momentum and charge]; > s.a. topology at cosmological scales.

In Quantum Mechanics > s.a. aharonov-bohm; Aharonov-Casher; theta sectors.
@ General references: Sudarshan et al AIHP(88); Balachandran et al 91; Aharonov & Reznik PRL(00)qp/99 [local/non-local complementarity].
@ Topology and quantum states: Balachandran Pra(01)qp/00-in; Dürr et al AHP(06)qp, JPA(07) [Bohmian mechanics]; > s.a. topology change.
@ Topology on space of states: Bugajski PLA(94).

In Quantum Field Theory > s.a. CPT [violation mechanism]; QCD.
@ General references: Monastyrsky 87; Schwarz 93, 94 [III, IV]; Bandyopadhyay 03.
@ Related topics: Blau IJMPA(89) [representation-independence]; Saaty ht/01 [topological charge]; Jackiw mp/05 [fractional quantum numbers, non-trivial phonons].

In Other Theories > s.a. canonical quantum gravity; Kink; knot theory in physics; spacetime topology.
@ String theory: Balachandran et al NPB(87).
@ Quantum topology: Isham CQG(89); Isham et al CQG(90); Isham in(91); Finkelstein & Hallidy IJTP(91) [and quantum logic]; Grib & Zapatrin IJTP(96)gq/95 [topology as an observable, and the space of topologies]; Schlesinger JMP(98); > s.a. quantum spacetime [relational topology].

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