Quaternions for GUTs

QUATERNIONS FOR GUTs

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.

Evidence For SUSY From GUTS? Evidence For GUTS From SUSY!

We review the theoretical and experimental status of minimal grand unified theories (GUTS), contrasting the failure of minimal non-supersymmetric SU(5) with the success of the minimal supersymmetric SU(5) and minimal supersymmetric Flipped SU(5)× U(1) models. We show that a reasonable value for the universal soft supersymmetry-breaking gaugino mass, 45GeV < m1/2 < 1TeV, and a 1−σ range of the o...

A god for guts.

Metrical Diophantine approximation for quaternions

The metrical theory of Diophantine approximation for quaternions is developed using recent results in the general theory. In particular, Quaternionic analogues of the classical theorems of Khintchine, Jarnı́k and Jarnı́k-Besicovitch are established. Introduction Diophantine approximation begins with a more quantitative understanding of the density of the rationals Q in the reals R. The starting p...

Hopf Mappings for Complex Quaternions

The natural mapping of the right quaternion vector space H onto the quaternion projective line (identified with the four-sphere) can be defined for complex quaternions H ⊗R C as well. We discuss its exceptional set, the fiber subspaces, and how the linear automorphism groups of two-dimensional quaternion vector spaces and modules induce groups of projective automorphisms of the image quadrics.