256 citations · 944 across the 58 of their papers we have counts for
9 papers · 1 filter
The Fermi gerbe of Weyl semimetals
Alan Carey, Guo Chuan Thiang
In the gap topology, the unbounded self-adjoint Fredholm operators on a Hilbert space have third homotopy group the integers. We realise the generator explicitly, using a family of…
Spectral flow of monopole insertion in topological insulators
Alan L. Carey, Hermann Schulz-Baldes
Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi pr…
Spectral flow for real skew-adjoint Fredholm operators
Alan L. Carey, John Phillips, Hermann Schulz-Baldes
An analytic definition of a -valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the ori…
On Index Theory for Non-Fredholm Operators: A -Dimensional Example
Alan Carey, Fritz Gesztesy, Galina Levitina +3
Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. Natural examples arise from -dimensional differential operators…
A noncommutative framework for topological insulators
Chris Bourne, Alan L. Carey, Adam Rennie
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of…
The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
Chris Bourne, Alan L. Carey, Adam Rennie
We prove the bulk-edge correspondence in -theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and bou…
Loop groups and quantum fields
Alan L. Carey, Edwin Langmann
This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in th…
Amenability of the Gauge Group
Alan Carey, Hendrik Grundling
Let G be one of the local gauge groups C(X,U(n)), C^\infty(X,U(n)), C(X,SU(n)) or C^\infty(X,SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial gro…
Loop groups, anyons and the Calogero-Sutherland model
Alan L. Carey, Edwin Langmann
The positive energy representations of the loop group of U(1) are used to construct a boson-anyon correspondence. We compute all the correlation functions of our anyon fields and s…