COUNTING NEGATIVE EIGENVALUES FOR THE MAGNETIC PAULI OPERATOR
We study the Pauli operator in a 2-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 bound to obtain a new formula on the number of eigenvalues of the magnetic Neumann Laplacian in the semiclassical limit. Our approach relies on reduction to a bou