2 citations · 5 across the 5 of their papers we have counts for
5 papers
A geometric algebra reformulation of 2x2 matrices: the dihedral group D_4 in bra-ket notation
Quirino M. Sugon, Carlo B. Fernandez, Daniel J. McNamara
We represent vector rotation operators in terms of bras or kets of half-angle exponentials in Clifford (geometric) algebra Cl_{3,0}. We show that SO_3 is a rotation group and we de…
Paraxial meridional ray tracing equations from the unified reflection-refraction law via geometric algebra
Quirino M. Sugon, Daniel J. McNamara
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 in…
Taxonomy of Clifford Cl_{3,0} subgroups: Choir and band groups
Quirino M. Sugon, Daniel J. McNamara
We list the subgroups of the basis set of Cl_{3,0} and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to +1 o…
Copernicus's epicycles from Newton's gravitational force law via linear perturbation theory in geometric algebra
Quirino M. Sugon, Sarah Bragais, Daniel J. McNamara
We derive Copernicus's epicycles from Newton's gravitational force law by assuming that a planet's orbit is a perturbed circular orbit, with the perturbation defined to be co-rotat…
Electromagnetic energy-momentum equation without tensors: a geometric algebra approach
Quirino M. Sugon, Daniel J. McNamara
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 derivat…