A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a nonlightlike curve and we find a reformulation of Frenet’s formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transpo...

We describe the local D=4 field theory on κ–deformed Minkowski space as nonlocal relativistic field theory on standard Minkowski space–time. For simplicity the case of κ-deformed scalar field φ with the interaction λφ is considered, and the κ–deformed interaction vertex is described. Supported by KBN grant 2P03B13012 On leave of absence from the Institute for Theoretical Physics, University of ...

We use a complex version of the celebrated Atiyah-Hitchin-DrinfeldManin matrix equations to construct admissible torsion-free sheaves on P3 and complex quantum instantons over our quantum Minkowski space-time. We identify the moduli spaces of various subclasses of sheaves on P3, and prove their smoothness. We also define the Laplace equation in the quantum Minkowski space-time, study its soluti...

This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a ...

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat metric. This generalizes the usual embedding widely used for the de Sitter models. I give the coordinate transformations for the embedding. Taking into account th...

The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which “flows equably without relation to anything external.” In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that he could provide a unified representation of space and time. With the pu...

By treating the real Maxwell Field and real linearized Einstein equations as being imbedded in complex Minkowski space, one can interpret magnetic moments and spinangular momentum as arising from a charge and mass monopole source moving along a complex world line in the complex Minkowski space. In the circumstances where the complex center of mass world-line coincides with the complex center of...