nLab Alan Carey

Alan Lawrence Carey

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Selected writings

Observation that vacua/ground states of the free Dirac field in a Coulomb background field are characterized by Fredholm operators whose index is the total charge in the vacuum:

• Alan Carey, Charles Angas Hurst, Denis O'Brien, Automorphisms of the canonical anticommutation relations and index theory, Journal of Functional Analysis 48 3 (1982) 360-393 $[$doi:10.1016/0022-1236(82)90092-1$]$

On spectral flow of self-adjoint Fredholm operators:

• Alan Carey, John Phillips: Fredholm modules and spectral flow J. Canadian Math. Soc. 50 (1998) 673-718 [cms:10.4153/CJM-1998-038-x]

On twisted K-theory:

• Alan Carey, Bai-Ling Wang: Thom isomorphism and Push-forward map in twisted K-theory, Journal of K-Theory 1 2 (2008) 357-393 (arXiv:math/0507414, doi:10.1017/is007011015jkt011)

On twisted differential K-theory:

• Alan Carey, Jouko Mickelsson, Bai-Ling Wang, Differential Twisted K-theory and Applications, Journal of Geometry and Physics, Volume 59, Issue 5, May 2009, Pages 632-653 (arXiv:0708.3114, doi:10.1016/j.geomphys.2009.02.002)

On spectral triples and index theory:

• Alan L. Carey, John Philips, Adam Rennie: Spectral Triples: Examples and Index Theory, in Alan Carey (ed.) Noncommutative Geometry and Physics, Renormalization, Motives, Index theory, Lectures in Mathematics and Physics, European Mathematical Society (2011) [doi:10.4171/008-1/5, ems:esi/95/1859, pdf]

On the bulk-edge correspondence for quantum Hall systems using Kasparov K-theory:

• Chris Bourne, Alan L. Carey, Adam Rennie: The bulk-edge correspondence for the quantum Hall effect in Kasparov theory, Lett Math Phys 105 (2015) 1253–1273 [doi:10.1007/s11005-015-0781-y, arXiv:1411.7527]

Related entries

• bundle gerbe

• Chern-Simons 2-gerbe

• noncommutative geometry

• quantum anomaly

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