Abstract:
In this senior project, vortex solutions of the fermionic system constrained in the (2+1)-dimensional spacetime by Cho, Kim and Park (CKP) [1] are reviewed. The existence of solutions comes from dynamics of the Dirac field coupled with pure Chern-Simons gauge field in the long distance limit. Motivated by the study of electromagnetic vortex solutions emerged from the gauged, nonlinear Schrodinger equation by Jackiw and Pi (JP) [2], we attempt to find a new vortex solution in the fermionic and relativistic system that also generates electric field. A well-defined solution has not been found so far, we instead investigate the possibility of a nonvanishing electric field solution in the fermionic system. First, we review the JP solutions and the vortex solutions from CKP construction in the non-relativistic limit provided by Duval, Horváthy and Palla (DHP) [3]. Then, we compare these two solutions and argue the origin of the electric field. Finally, we conclude all the results obtained from these three theories.
