Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative $\kappa$-Minkowski space-time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard-Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of $\kappa$-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.