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) 

Spinors and gravity without Lorentz indices 
Abstract  Coupling spinor fields to the gravitational field, in the setting of general relativity, is standardly done via the introduction of a vierbein field and the (associated minimal) spin connection field. This makes three types of indices feature in the formalism: world/coordinate indices, Lorentz vector indices, and Lorentz spinor indices, respectively. This article will show, though, that it is possible to dispense altogther with the Lorentz indices, both tensorial ones and spinorial ones, obtaining a formalism featuring only world indices. This will be possible by having both the 'Dirac operator' and the generators of 'Lorentz' transformations become spacetimedependent, although covariantly constant. The formalism is developed in the setting of complexified quaternions. 

Freely available at  arxiv.org/abs/1811.00377 

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 

