We list the subgroups of the basis set of Cl3,0 and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to Â±1, (2) the generatorsâ€¦ (More)

We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the rayâ€™s 2Ã—2 matrix operators should be right-acting, soâ€¦ (More)

In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of theâ€¦ (More)

We represent vector rotation operators in terms of bras or kets of half-angle exponentials in Clifford (geometric) algebra Cl3,0. We show that SO3 is a rotation group and we define the dihedral groupâ€¦ (More)

We derive the paraxial meridional ray tracing equations from the unified reflection-refraction law using geometric algebra. This unified law states that the normal vector to the interface is aâ€¦ (More)

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson andâ€¦ (More)

In this paper, we use Clifford (geometric) algebra Cl(3,0) to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane wavesâ€¦ (More)

We derive Copernicusâ€™s epicycles from Newtonâ€™s gravitational force law by assuming that a planetâ€™s orbit is a perturbed circular orbit, with the perturbation defined to be co-rotating with the saidâ€¦ (More)

We use the vector wedge product in geometric algebra to show that Poisson commutator brackets measure preservation of phase space areas. We also use the vector dot product to define the Poissonâ€¦ (More)