physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
In analogy to how 3d TQFTs are induced from quantum groups/Hopf algebras/ and generally bialgebras (hence 3-modules, the higher space of quantum states assigned to the point which by the cobordism theorem defines the theory) one may build 4d TQFTs from higher analogs of these, namely models of 4-modules given by algebraic structures such as trialgebras and Hopf categories.
Original references:
Louis Crane, Louis Kauffman, David Yetter, State-Sum invariants of 4-manifolds I, Journal of Knot Theory and Its Ramifications Vol. 06, No. 02, pp. 177-234 (1997) (arXiv:hep-th/9409167, pdf, doi:10.1142/S0218216597000145)
Louis Crane, Igor Frenkel, Four dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35 (1994) 5136-5154, (arXiv:hep-th/9405183)
See also
Construction via factorization homology from braided tensor categories (with relation to double affine Hecke algebras) is discussed in
From fully dualizable braided tensor categories, via the cobordism hypothesis:
As descriptions of topological insulators/topological phases of matter:
Kevin Walker, Zhenghan Wang, (3+1)-TQFTs and Topological Insulators, Frontiers of Physics volume 7, pages 150–159 (2012) (arXiv:1104.2632, doi:10.1007/s11467-011-0194-z)
(see Walker-Wang model)
Clement Delcamp, Excitation basis for (3+1)d topological phases, Journal of High Energy Physics 2017 (2017) 128 (arXiv:1709.04924 doi:10.1007/JHEP12(2017)128)
Many more references should eventually go here…
Last revised on May 23, 2021 at 04:45:22. See the history of this page for a list of all contributions to it.