Stationary states for fermions in an external electric field

Abstract We present a relativistic analysis of fermions in an external electric field by non-perturbatively solving the Dirac equation with a static gauge. Different from the magnetic field effect, the fermion wave function in an electric field oscillates asymptotically, which results in the absence of bound states in an infinite system. For a confined fermion, the confinement is gradually canceled by the electric field, and the fermion becomes deconfined when the electric coupling is stronger than the confinement coupling. However, a fermion in an electric field can be confined to a finite system by applying the MIT bag boundary condition, namely, the disappearing normal component of the probability current at the boundary. The solutions obtained can serve as a basis for calculating dynamical processes in the presence of a strong electric field, such as those occurring in the early stage of relativistic heavy-ion collisions, where an extremely strong electric field is expected to be generated.