Spinor fields without Lorentz frames in curved spacetime using complexified quaternions 
Abstract  Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated, might be related to electromagnetism, emerges naturally. 

Published in  J. Math. Phys. 50, 083507 (2009) 

Freely available at  arxiv.org/abs/0811.1357 

Exponentiation of the spinor representation of the Lorentz group 
Abstract  An exact finite expression for the exponentiation of the (spin 1/2) spinor representation of the Lorentz group is obtained. From this expression an exact finite expression for the exponentiation of the vector representation of the Lorentz group is derived. The two expressions are compared with the literature in the special cases of either spatial rotations or boosts, only. 

Published in  J. Math. Phys. 42, 4497 (2001) 

Comment on “Wilson loops in fourdimensional quantum gravity” 
Abstract  As an example of a classical holonomy Modanese [Phys. Rev. D 49, 6534 (1994)] considered a class of circular curves in Schwarzschild geometry. The result obtained does not, as it should, vanish in the limit M=0. This Comment corrects this error. 

Published in  Phys. Rev. D 64, 088501 (2001) 

Electroweak interaction without helicity projection operators using complexified octonions 
Abstract  Using complexified octonions, a formalism seemingly capable of describing the coupling of spinors to the electroweak force without helicity projection operators is presented. 

Freely available at  arxiv.org/abs/1011.5633 

Spinor fields without Lorentz frames in curved spacetime using complexified quaternions 
Abstract  Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated, might be related to electromagnetism, emerges naturally. 

Freely available at  arxiv.org/abs/0811.1357 

Natural octonionic generalization of general relativity 
Abstract  An intriguingly natural generalization, using complex octonions, of general relativity is pointed out. The starting point is the vierbeinbased double dual formulation of the EinsteinHilbert action. In terms of two natural structures on the (complex) quaternions and (complex) octonions, the inner product and the cross products, respectively, this action is linked with the complex quaternionic structure constants, and subsequently generalized to an achtbeinbased 'double chidual' action in terms of the complex octonionic structure constants. 

Freely available at  arxiv.org/abs/0707.0554 

