Abstract
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
Highlights
In recent years we have been scrutinizing Planck scale Physics through many theories, proposals, ideas, etc., all this effort expended in order to improve our understanding of the Nature behaviour at shortest distances
An interesting outcome of these proposals is the presence of a minimal measurable length scale [2], this can be incorporated to the quantum theory by the so-called Generalized Uncertainty Principle [3,4,5]
In this paper we have studied a very special relativity (VSR) inspired modification of Maxwell–Chern–Simons electrodynamics
Summary
In recent years we have been scrutinizing Planck scale Physics through many theories, proposals, ideas, etc., all this effort expended in order to improve our understanding of the Nature behaviour at shortest distances (as well as in the beginning of our Universe [1]). Among the most interesting analyses involving VSR effects we can cite a realization of VSR via a lightlike noncommutative deformation of Poincaré symmetry [14], studies on Dirac equation [15] and hydrogen atom [16], as well as gauge theories [17] and curved spacetime field theories [18], gravitational and cosmological models [19,20]. With this discussion we see that a massive gauge field, defined in terms of the ordinary derivative, can be described suitably in a gauge-invariant fashion when written in terms of the wiggle operator This may be considered our starting point in defining our model of interest
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