Introduction

Abstract

In this book we are concerned with symmetry properties of Maxwell’s equations and of other differential equations which are in some way related to the fundamental equations of electrodynamics. The classical results of Lorentz, Poincaré, Einstein, Heaviside, Larmor, Bateman, Cunningham, and Rainich are obtained by means of a unified algebraic-theoretical approach, and also symmetry properties of Maxwell’s equations (additional invariance under the group U(2) ⊗ U(2) and the twenty-three dimensional Lie algebra A₂₃) unknown until ([111, 67, 115]) are also established. Moreover, the symmetry properties of the Dirac equations are analyzed, and conformal transformations for massless fields with arbitrary spin are found in explicit form. Finally, some inverse problems of algebraic-theoretical analysis are solved which consist in the description of all possible (up to equivalence) linear equations invariant under a given Lie algebra.

Mathematics loves symmetry above all

J.C. Maxwell