Spinor-Like Hamiltonian for Maxwellian Optics

Abstract

Background Spinors are more special objects than tensor. Therefore possess more properties than the more generic objects such as tensors. Group of Lorentz two-spinors is the covering group of the Lorentz group. Purpose Since the Lorentz group is a symmetry group of Maxwell’s equations, it is assumed to reasonable to use when writing the Maxwell equations Lorentz two-spinors and not tensors. Method We write the Maxwell equations using Lorentz two-spinors. Also used a convenient representation of Lorentz two-spinors in terms of the Riemann- Silberstein’s complex vectors. Results In the spinor formalism (in the representation of the Lorentz spinors and Riemann-Silberstein’s vectors) we have constructed the Hamiltonian of Maxwellian optics. With the use of spinors Maxwell’s equations take the form similar to the Dirac equation. Conclusions For Maxwell’s equations in the Dirac-like form we can expand re- search methods at the expense of the methods of quantum field theory. In this form, clearly visible the connection between the Hamiltonians of geometric, beam and Maxwellian optics.

Type
Publication
EPJ Web of Conferences