Related papers: Aharonov-Casher theorems for Dirac operators on ma…
We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an…
Under two boundary conditions, the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized -Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on…
We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a "geometric Witt condition". We accomplish this by cutting off to a smooth manifold with boundary, applying the…
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.
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.
We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual $\bA\in L^2_{loc}$ condition on the…
Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional…
The Aharonov--Casher (AC) effect describes the geometric phase acquired by a neutral particle carrying a magnetic dipole moment moving in an external electric field. In supersymmetric gauge theories it is often argued that exact…
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of…
We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection…
Along the lines of the classic Hodge-De Rham theory a general decomposition theorem for sections of a Dirac bundle over a compact Riemannian manifold is proved by extending concepts as exterior derivative and coderivative as well as as…
The spectral properties of the Dirac Hamiltonian in the the Aharonov-Bohm potential are discussed. By using the Krein-Friedel formula, the density of states (DOS) for different self-adjoint extensions is calculated. As in the…
Functional determinants for Dirac operators on manifolds with boundary are considered. Ellipticity of boundary value problems is discussed in terms of the Calderon projector. The functional determinant for a Dirac operator on a…
Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy…
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower…
We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is…
Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of…
Topological flat moir\'e bands with nearly ideal quantum geometry have been identified in homobilayer transition metal dichalcogenide moir\'e superlattices, and are thought to be crucial for understanding the fractional Chern insulating…
We establish that the Pauli operator describing a spin-1/2 two-dimensional quantum system with a singular magnetic field has, under certain conditions, an infinite-dimensional space of zero modes, possibly, both spin-up and spin-down,…
Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS eta invariant in the presence of torsion. The bulk…