Dirac equation in magnetic-solenoid field
نویسندگان
چکیده
We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann’s theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.
منابع مشابه
Dirac spinors in solenoidal field and self adjoint extension of its Hamiltonian
The magnetic field of an infinitely long solenoid is immensely important for various reasons. For example, it is used to study the Aharanov-Bohm [1] effect. Similarity with this field also helps one to understand the physics of cosmic strings [2]. It is therefore important to study the quantum mechanics of a Dirac fermion in the field of an infinitely long solenoid, which is what we do in the p...
متن کاملar X iv : m at h - ph / 0 31 00 07 v 1 7 O ct 2 00 3 Green functions of the Dirac equation with magnetic - solenoid field
Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2 + 1 and 3 + 1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as ...
متن کاملGreen Functions of the Dirac Equation with Magnetic–Solenoid Field
Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2 + 1 and 3 + 1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as ...
متن کاملDirac fermions in a magnetic-solenoid field
We consider the Dirac equation with a magnetic-solenoid field (the superposition of a solenoid field and a collinear uniform magnetic field). Using von Neumann’s theory of the selfadjoint extensions of symmetric operators, we construct selfadjoint Dirac Hamiltonians for the case of the Aharonov-Bohm solenoid in 2 + 1 and 3 + 1 dimensions. Each extension of the family is specified by certain asy...
متن کاملNon-Relativistic Limit of Neutron Beta-Decay Cross-Section in the Presence of Strong Magnetic Field
One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is ...
متن کامل