  (abbreviated) I will describe my work on proton Compton scattering in a
Unified Proton-Delta theory and on the computation of scattering amplitudes in
Yang-Mills theory.
  We study proton Compton scattering in the first resonance region in an
effective field theory approach with adviser Dr. Konstantin G. Savvidy. Proton
and $\Delta^+$ are naturally unified in the generalized Rarita-Schwinger theory
proposed by Savvidy. We introduce six non-minimal electromagnetic
interactions--with their coefficients being called "form factors"--and bare
polarizabilities in an effective Lagrangian. We express proton and Delta
magnetic moments and the electromagnetic polarizabilities in terms of the bare
polarizabilities and the form factors. We fit the form factors and bare
polarizabilities using experimental data and derive Delta magnetic moment from
the best fit values of the parameters.
  Then I present our joint work with adviser Dr. Gang Chen on the study of
boundary behavior of off-shell Yang-Mills amplitudes with a pair of external
momenta complexified. In Feynman gauge, we introduce a set of "reduced
vertices" which can capture the boundary behavior up to the first two leading
orders. We then prove a theorem on permutation sum for a given color ordering,
and use it to analyze the boundary behavior of amplitudes with two non-adjacent
legs complexified. Then we construct off-shell Britto-Cachazo-Feng-Witten
(BCFW) recursion relations and study relations between off-shell amplitudes.
  Finally, we study the recursion relations for off-shell Yang-Mills amplitudes
at tree and one loop levels as deduced from imposing complexified Ward
identity, also in collaboration with Dr. Gang Chen.
