On the Dirac and Pauli Operators with Several Aharonov-bohm Solenoids
نویسنده
چکیده
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 Aharonov-Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invariant, and this operator does not have any zero-modes.
منابع مشابه
Program of a Mini - Course “ Resonances and Threshold Singularities for Magnetic Quantum Hamiltonians ”
1. Basic facts from the spectral theory of magnetic quantum Hamilto-nians (Schrödinger, Pauli, and Dirac operators with magnetic fields): self-adjointness, gauge invariance, diamagnetic inequality, Aharonov-Casher theorem [1, 7]. Constant magnetic fields [1]. 2. Berezin-Toeplitz operators and pseudodifferential operators with con-4. Resonances for the 3D Schrödinger operator with constant magne...
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