Localized solutions for the massive Thirring model in the presence of an external electrostatic field

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Abstract
We investigate the classical equations of motion for the massive Thirring model in one space and one time dimension in the presence of an external electrostatic field. It is shown that stationary-confined solutions are acceptable for this model if a self-consistency condition is satisfied. We suggest the possibility of solving the equations of motion using a perturbative approach for the electromagnetic interaction. Some properties of the first-order contribution to the solution, which are fully independent of the external potential shape, are exhibited. A specific example is also developed and analyzed.

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