Zobrazeno 1 - 10
of 92
pro vyhledávání: '"Carey, Alan L."'
In this article we give a comprehensive treatment of a `Clifford module flow' along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO${}_{*}(\mathbb{R})$ via the Clifford index of Atiyah-Bott-Shapiro. We dev
Externí odkaz:
http://arxiv.org/abs/1907.04981
Autor:
Carey, Alan L., Rennie, A.
We offer a short proof of Connes' Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors' extensive work on a refined version of the local index formula, and
Externí odkaz:
http://arxiv.org/abs/1803.02600
Autor:
Carey, Alan L., Schulz-Baldes, Hermann
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 projection. This paper establishes a generalization to higher even dimen
Externí odkaz:
http://arxiv.org/abs/1705.04162
An analytic definition of a $\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through $0$ alo
Externí odkaz:
http://arxiv.org/abs/1604.06994
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 noncommutative index theory of operator algebras. In particular we fo
Externí odkaz:
http://arxiv.org/abs/1509.07210
We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological
Externí odkaz:
http://arxiv.org/abs/1411.7527
Autor:
Benameur, Moulay-Tahar, Carey, Alan L.
Given a smooth fibration of closed manifolds and a family of generalised Dirac operators along the fibers, we define an associated bivariant JLO cocycle. We then prove that, for any $\ell \geq 0$, our bivariant JLO cocycle is entire when we endow smo
Externí odkaz:
http://arxiv.org/abs/1108.4528
Autor:
Carey, Alan L., Langmann, Edwin
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 the discussion is the construction of quantum fields using vertex operat
Externí odkaz:
http://arxiv.org/abs/1007.1629
Autor:
Carey, Alan L., Wang, Bai-Ling
In this paper, we establish the Riemann-Roch theorem in twisted K-theory extending our earlier results. As an application, we prove a twisted index formula and show that D-brane charges in Type I and Type II string theory are classified by twisted KO
Externí odkaz:
http://arxiv.org/abs/0909.4848
We study an example of an index problem for a Dirac-like operator subject to Atiyah-Patodi-Singer boundary conditions on a noncommutative manifold with boundary, namely the quantum unit disk.
Externí odkaz:
http://arxiv.org/abs/0901.0123