On the Aharonov-Bohm Hamiltonian

Classical Electrodynamics without Fields and the Aharonov-Bohm effect

The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In agreement with the standard Maxwell-Lorentz theory, the force acting on electrons from infinite solenoids or ferromagnetic rods vanishes. However, the interaction energies and phase factors of the electron wave packets are non-zero. This allows us to explain the Aharonov-Bohm effect without involvement of electromagneti...

Lieb-thirring Inequality for the Aharonov-bohm Hamiltonian and Eigenvalue Estimates

The Friedrichs Extension of the Aharonov-bohm Hamiltonian on a Disc

We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension HF corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for HF .

The Dirac Hamiltonian in an Aharonov - Bohm gauge field and its self - adjoint extensions Kazuhiko ODAKA ∗ and Kazuya SATOH

By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by a 2 × 2 unitary matrix. ∗e-m...

Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect

We construct a classical action for a system of N point-like sources which carry SU(2) non-Abelian charges coupled to non-Abelian Chern-Simons gauge fields, and develop a quantum mechanics for them. Adopting the coherent state quantization and solving the Gauss’ constraint in an appropriately chosen gauge, we obtain a quantum mechanical Hamiltonian given in terms of the Knizhnik-Zamolodchikov c...