A Spinor Model for Cascading Two-port Scattering Matrices In Conformal Geometric Algebra

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port scattering matrix as a rotation in four dimensional Minkowski space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional microwave network theory. Techniques to translate two-port scattering matrix in and out of spinor form are given. Once the translation is laid out, geometric interpretations are given to the physical properties of reciprocity, loss, and symmetry and some mathe- matical groups are identified. Methods to decompose a network into various sub-networks, are given. An example application of interpolating a 2-port network is provided demonstrating an advantage of the spinor model. Since rotations in four dimensional Minkowski space are Lorentz transformations, this model opens up the field of network theory to physicists familiar with relativity, and vice versa.

ELKO SPINOR MODEL WITH TORSION AND COSMOLOGY

We investigate the cosmology of ELKO spinor model when minimal coupling with torsion is included. Unlike the Dirac spinor which interacts only with the totally anti-symmetric components of torsion tensor, we find the interaction of the time component of the trace of torsion tensor with ELKO spinor provides different aspects of cosmology with fermions. We discuss a couple of cases with given potentials of ELKO spinor which can result in interesting cosmological consequences. Especially, we show that there exists an exact cosmological solution in which the universe began its acceleration only recently and this solution is an attractor. This corresponds to specific forms of torsion and potential with a mild fine-tuning which can address the coincidence problem.