On the new invariance algebras of relativistic equations for massless particles

The authors show that the massless Dirac equation and Maxwell equations are invariant under a 23-dimensional Lie algebra, which is isomorphic to the Lie algebra of the group C 4 (X)U(2)(X)U(2). It is also demonstrated that any Poincare-invariant equation for a particle of zero mass and of discrete spin provide a unitary representation of the conformal group and that the conformal group generators may be expressed via the generators of the Poincare group.