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The main motivation to study models in the presence of a minimal length is toobtain a quantum field theory free of the divergences. In this way, in thispaper, we have constructed a new framework for quantum electrodynamics embeddedin a minimal length scale background. New operators are introduced and theGreen function method was used for the solution of the field equations, i.e.,the Maxwell, Klein-Gordon and Dirac equations. We have analyzed specificallythe scalar field and its one loop propagator. The mass of the scalar fieldregularized by the minimal length was obtained. The QED Lagrangian containing aminimal length was also constructed and the divergences were analyzed. Theelectron and photon propagators, and the electron self-energy at one loop as afunction of the minimal length was also obtained.

Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale