6 citations · 13 across the 11 of their papers we have counts for
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Poisson commutator-anticommutator brackets for ray tracing and longitudinal imaging via geometric algebra
Quirino M. Sugon, Daniel J. McNamara
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 defin…
Revisiting 2x2 matrix optics: Complex vectors, Fermion combinatorics, and Lagrange invariants
Quirino M. Sugon, Daniel J. McNamara
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 ray's 2x2 matrix operators should be…
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…