# Theoretical Physics

**FACULTY **

- Fr. Daniel J. McNamara, S.J., Ph.D. (Professor) (Geometric Algebra)(on leave)
- Dr. Jerrold Garcia (Associate Professor) (Neural Networks and General Relativity)
- Dr. Quirino M. Sugon Jr. (Assistant Professor) (Geometric Algebra)
- Clint Bennett (Ph.D. Candidate) (Chaos Theory) (on Faculty Development Grant)
- Joel Maquiling (Ph.D. Candidate) (Geometric Algebra)

**STUDENTS**

Adler Santos (M.S. student) (Electromagnetic Stokes parameters of elliptically polarized light via geometric algebra)

Michael Andrews (M.S. student) (Molecular vibrational spectroscopy via geometric algebra)

Michael Sulangi (M.S. student) (Quantum Mechanics of Topological Surfaces)

**PUBLICATIONS**

**ISI Journals**

Michelle Wynne C. Sze, Quirino M. Sugon, Jr., and Daniel J. McNamara, “Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?,” J. Opt. Soc. Am. A 27, 2468-2479 (2010). doi:10.1364/JOSAA.27.002468

Quirino M. Sugon Jr. and Daniel J. McNamara, “A geometric algebra reformulation of geometric optics,” Am. J. Phys. **72**(1), 92-97 (2004).

Christopher Monterola, May Lim, Jerrold Garcia, and Caesar Saloma, Feasibility of a neural network as a classifier of undecided respondents in a public opinion survey, in International Journal of Public Opinion Research **14** (2), 222-229 (2002).

Rafael Saldaña, Jerrold Garcia, Felix Muga II, William Yu, “Development of a Beowulf-Class High Performance Computing System for Computational Science Applications,” Science Diliman, Vol 13, No 2 (2001).

**Book Chapters**

Quirino M. Sugon Jr. and Daniel J. McNamara, “Ray tracing in spherical interfaces using geometric algebra,” Advances in Imaging and Electron Physics, ed. by Peter W. Hawkes, **139**, pp. 179-224 (2006).

Quirino M. Sugon Jr. and Daniel J. McNamara, “A Hestenes spacetime algebra approach to light polarization,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by L. Dorst, C. Doran, and J. Lasenby (Birkhauser, Boston, 2002), pp. 297-315.

**ArXiv**

Quirino M. Sugon Jr. and Daniel J. McNamara, “Poisson commutator-anticommutator brackets for ray tracing and longitudinal imaging via geometric algebra,” arXiv:0812.2979v1 [math-ph] (16 Dec 2008). 10 pages, 9 figures.

Quirino M. Sugon Jr. and Daniel J. McNamara, “Revisiting 2×2 matrix optics: Complex vectors, Fermion combinatorics, and Lagrange invariants,” arXiv:0812.0664v1 [physics.optics] (3 Dec 2008).

Quirino M. Sugon Jr., Carlo B. Fernandez, and Daniel J. McNamara, “A geometric algebra reformulation of 2×2 matrices: the dihedral group D_4 in bra-ket notation,” arXiv:0811.3680v1 [math-ph] (24 Nov 2008).

Quirino M. Sugon Jr. and Daniel J. McNamara, “Paraxial meridional ray tracing equations from the unified reflection-refraction law via geometric algebra,” arXiv:0810.5224v1 [physics.optics] (29 Oct 2008).

Quirino M. Sugon Jr. and Daniel J. McNamara, “Taxonomy of Clifford *Cl*_{3,0} subgroups: choir and band groups,” arXiv:0809.0351v1 [math-ph] (2 Sep 2008).

Quirino M. Sugon Jr., Sarah Bragais, and Daniel J. McNamara, “Copernicus’s epicycles from Newton’s gravitational force law via linear perturbation theory in geometric algebra,” arXiv:0807.2708v1 [physics.space-ph] (17 Jul 2008).

Quirino M. Sugon Jr. and Daniel J. McNamara, “Electromagnetic energy-momentum equation without tensors: a geometric algebra approach,” arXiv:0807.1382v1 [physics.class-ph] (9 Jul 2008).

**Undergraduate Thesis**

Reinabelle R. Reyes . Undergraduate Thesis: “Successive Lorentz boosts: Equivalent boost and rotation using geometric algebra.” Presented in Samahang Pisika ng Pilipinas Conference (SPP)

Sarah Bragais. Undergraduate thesis: Copernicus’s epicycles from Newton’s gravitational force law via linear perturbation theory in geometric algebra. (ArXiv)

Evan Vidal Sagge. Undergraduate thesis: “3D reconstruction from 2D stereo images”. Presented in Samahang Pisika ng Pilipinas Conference.

Carlo B. Fernandez. Undergraduate thesis: “Computing the products of elements of crystallographic point groups using quaternions.” (Related article Dihedral Group D4 is published in ArXiv)

Jong Silverio. Undergraduate Thesis: “Kinematics on the surface of rotating earth using quaternions.”

Marvin Go. Undergraduate thesis: “Interpolation of 2D velocity fields using geometric algebra.”

Jason Angeles. Undergraduate Thesis: “Ray tracing model of beam waists”

Mark Dizon. Undergraduate Thesis: “Kinematics of the double pendulum using geometric algebra.” S