Gauge Invariant Fractional Electromagnetic Fields

Details Gauge Invariant Fractional Electromagnetic Fields Gauge Invariant Fractional Electromagnetic Fields

2011-08-17

arxiv.org/abs/1108.3493v1

Phys.Lett.A375:3541-3546,2011

Physics

Mathematical Physics

accepted for publication in Physics Letters A

Scientific paper

10.1016/j.physleta.2011.08.033

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

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