My Publications

First Author

Solution to Feshbach--Villars spin-1/2 equation for bound & resonant states using matrix continued fractions

First nontrivial numerical solution to this equation ever published. Uses nonrelativistic representation with experimentally relevant short range potentials, also finds confinement states for quarks. FV12

Solution to Feynman--Gell-mann equation for bound & resonant states using hypergeometric functions

Demonstrating the method of using hypergeometric functions to analytically invert the infinite Hamiltonian to a finite Green's operator, then find numerical solutions to experimentally relevant short range potentials. FG

Thesis where this and surrounding theory is derived from first principles

I derive all the relevant relativistic quantum mechanics equations from first principles and present the solution methods. Using the Weyl representation, I derived the equivalent analytic continuation of the angular momentum, used with the Feynman--Gell-mann equation, for the 8-component Feshbach-Villars spin-1/2 equation by proving (not formally, sorry mathematicians) the proper limit behavior of the matrix continued fraction. This demonstrates the power of the Weyl representation over standard or the nonrelativistic representation when dealing with angular momentum coupling, as the total coupling is contained within each spinor block (total coupling decouples to local spinorL/R coupling ie block diagonal). The block diagonal structure is what allows the analytic continuation elegantly. Thesis

Collaborator

Single-View Tomographic Reconstruction Using Learned Primal Dual

Single-view tomographic reconstructions of axially-symmetric targets for two modalities. The first assumes low-divergence or parallel X-rays and the second models a cone-beam X-ray imaging testbed LPD