I am interested in the various symmetries characterizing certain scalar and gauge field theories, and the ways those often manifest themselves as hidden mathematical properties of their scattering amplitudes.
During my graduate studies at the University of North Carolina at Chapel Hill, my PhD advisor, Prof. Louise Dolan, and I shed some light on the Yangian extension of the conformal group SO(2,n), where n is the number of space-time dimensions. We established the closure of the SO(2,n) Yangian algebra for a differential operator representation in momentum-space, by proving that the Serre relation is satisfied for both scalar and gauge fields, in their respective domains of applicability. We also studied the action of the SO(2,n) Yangian generators on the tree-level scattering amplitudes of scalar ฮป ฯ3 theory and pure Yang-Mills theory; two non-supersymmetric field theories which are intimately related through the Cachazo-He-Yuan scattering equations formalism. A more detailed presentation of our work can be found in my doctoral dissertation.
To facilitate my research, I have made extensive use of Mathematica and its computer algebra capabilities. I have developed Mathematica packages for symbolically calculating the action of the conformal SO(2,n) Yangian generators on the above mentioned scalar and gauge theory tree amplitudes, and also for numerically evaluating those using finite fields methods, i.e. using modular arithmetic with large prime numbers. I plan on publishing these packages on my GitHub profile, for use by the rest of the scattering amplitudes community.
