Spinor electromagnetism in isotropic chiral media (Q1894784)

The author presents a formalism where the electromagnetic field is represented by traceless second rank spinor fields and applies the theory to isotropic chiral media. The theory is covariant under the group \(SL (2, \mathbb{C})\) (the universal covering group of the homogeneous restricted and orthocronous Lorentz group). This presentation is important since the usual tensor formulation of electromagnetism is more symmetric than required by relativity since the Maxwell equations are covariant with respect to reflections in space time. This has been discussed by \textit{M. Sachs} [Found. Phys. 10, 921 (1988)] who uses instead of traceless second rank spinor fields the Dirac spinor fields. However Sachs' presentation has the drawback of not being manifestly covariant. Indeed \textit{W. A. Rodrigues} and \textit{E. C. de Oliveira} [Int. J. Theor. Phys. 32, 948-955 (1993)] proved that Sachs' spinor field representing the electromagnetic field depends on the choice of a particular idempotent field defined by a particular reference frame field in the Clifford algebra bundle of a Minkowski space time. Some interesting applications of the author's formalism is given and it seems that this formalism is more simple in applications than the complex electromagnetism earlier presented by the author [Phys. Rev. E 47, 136 (1993)].