Physics NotePublished
Numerical Studies of Relativistic Corrections to Fermion Dynamics and the Aharonov-Casher Effect
L. G. Ferreira Filho; José Abdalla Helayel Neto; José Luis Chauca Murga; Grupo de Física Teórica José Leite Lopes
2004
Publication details
- Authors
- L. G. Ferreira Filho; José Abdalla Helayel Neto; José Luis Chauca Murga; Grupo de Física Teórica José Leite Lopes
- Type
- Physics Note
- Status
- Published
- Publication date
- 2004
- Description
- Dirac's equation with minimal eletromagnetic coupling yields, in the weakly relativistic regime, the Pauli's equation for two-component minimally-interacting electron endowed with magnetic moment coupling and the right value of the Land\'{e} g-factor, g=2. On the other hand, another remarkable feature associated with spinning particles is the coupling of the magnetic dipole moment to an electric field, which gives rise to the so-called Aharonov-Casher phase for the wave function of the test particle. This phase shift shows up even though there is no force acting on the particle, just as in the familiar case of the Aharonov-Bohm effect. The most accurate experimental measurements of the spin-electric field interaction are carried out with atomic systems. This work sets out to investigate how the Aharonov-Casher effect may be related to the relativistic regime: in practical terms, how it may appear by means of relativistic corrections to the Schr\"{o}dinger equation, once an external eletromagnetic field is switched on. One should understand at which order of velocities the Aharonov-Casher shift arises, either by adding up higher-order gradient terms to the Schr\"{o}dinger equation or by carring out the non-relativistic limit of Dirac's equation with higher-derivative terms. The latter has very interesting consequences whenever adjoined to the Dirac's equation, leading to a rich excitation spectrum and inducing interesting couplings in the low-energy regime. In view of the calculational complexity inherent to the task of finding solutions to these higher-derivatives partial differential equations, wave-function solutions and phase shifts have to be searched for with the help of numerical methods and computer-algebra softwares.
- Year
- 2004
- Number
- CBPF-NF-012/04
- Linked to a thesis
- No
- Linked to a grant
- No