Abstract
Two Maxwell-Chern-Simons (MCS) models in the (1 + 3)-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE) model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.
Highlights
There are three motivations of the present paper
In an analogous way we have found the maximal Lie group and discrete symmetries admitted by system (12)–(14)
One of important applications of Lie symmetries to partial differential equations (PDE) is connected with constructing their exact solutions
Summary
There are three motivations of the present paper. First we search for four-dimensional formulations of Maxwell-Chern-Simon models [1]. There are two symmetries of Maxwell’s electrodynamics that have dominated all fundamental physical theories, namely, gauge and Lorentz invariance They provide physical principles that guide the invention of models describing fundamental phenomena. Aν where Fμν = ∂μAν − ∂ν Aμ is the tensor of e.m. field and Aν is the four-vector of the photon field This field Aν is massive and so the gauge invariance is lost. The CFJ model presents a rather elegant and convenient way for testing possible violation of the Lorentz-invariance, which causes its large impact. This model has a principle disadvantage, namely, the breaking of the Lorentz-invariance “by hands” and the additional constants pμ have no physical meaning. This Lagrangian is not affected by the change A4 → A4 + C, where C is a constant. In non-relativistic approximation, Lagrangian (3) is reduced to the Galilei-invariant Lagrangian for the irreducible Galilean field discussed in [3]
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