DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

Poincare inequalities are a simple way to obtain lower bounds on the distortion of mappings X into Y. These are shown below to be sharp when we consider the Lp spaces. A Poincare inequality is one of the following type: suppose Ψ : [0, ∞) → [0, ∞) is a nondecreasing function and that au,v, bu,v are finite arrays of real numbers (for u, v ∈ X, and not all of the numbers 0). We say that functions...

New time dependent wave solutions to the classical homogeneous Maxwell equations in the vacuum have been found. These waves are not transverse; they exhibit both torsion and spin; they have ̄nite magnetic helicity, A ± B 6= 0, a non-zero Poynting vector, E £H 6= 0;and a non zero second Poincare invariant, E ± B 6= 0: Two four component rank 3 tensors, constructed on topological grounds in terms ...

It is shown how, by carrying out a sequence of three coordinate axis rotations in Poincare space, one can calculate the principal basis and the real, nonnegative eigenvalues of any symmetric polarization scattering matrix. Then the two eigenvalues and the three Eulerian angles of the principal axes in Poincare space constitute a complete set of pure scatterer parameters. A scatterer classificat...

Following the construction of the κ-Minkowski space from the bicrossproduct structure of the κ-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a fivedimensional differ...