Abstract
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.
Highlights
The Dirac equation for a charge in an external electromagnetic field is the basic equation for relativistic quantum mechanics and quantum electrodynamics
We explored the integrability features of the Dirac equation with an external electromagnetic field by means of the noncommutative integration method and the method of separation of variables in terms of external fields of special form
We studied changes of the subalgebras of symmetry operators that are used to construct exact solutions of the Dirac equation with an external field, compared to the subalgebras of the free Dirac equation
Summary
The Dirac equation for a charge in an external electromagnetic field is the basic equation for relativistic quantum mechanics and quantum electrodynamics. To construct exact solutions of the Dirac equation, the separation of variables method (SoV) is commonly used. The external electromagnetic fields admitting SoV in the Dirac and the Klein–Gordon equations have been listed in refs [1, 2]. Integration of the free Dirac equation using the NI method was considered in refs.
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