Formulation of Galilean relativistic Born-Infeld theory

In this paper, we formulate, for the first time, in a systematic manner, Galilean relativistic Born-Infeld action in detail. Exploiting maps connecting Lorentz relativistic and Galilean relativistic vectors, we construct the two limits (electric and magnetic) of Galilean relativistic Born-Infeld action from usual relativistic Born-Infeld theory. An action formalism is thereby derived. From this action, equations of motion are obtained either in the potential or field formulation. Galilean version of duality transformations involving the electric and magnetic fields are defined. They map the electric limit relations to the magnetic ones and vice-versa, exactly as happens for Galilean relativistic Maxwell theory. We also explicitly show the Galilean boost and gauge invariances of the theory in both limits.