Hamiltonian formulation of Jackiw-PI three-dimensional gauge theories

A three-dimensional non-Abelian gauge theory was proposed by Jackiw and Pi to create mass for the gauge fields. However, the quadratic action obtained by switching off the non-Abelian interactions possesses more gauge symmetries than the original one, causing some difficulties in quantization. Jackiw and Pi proposed another action by introducing new fields, whose gauge symmetries are consistent with the quadratic part. It is shown that all of these theories have the same number of physical degrees of freedom in the Hamiltonian framework. Hence, as far as the physical states are considered, there is no inconsistency. Nevertheless, perturbation expansion is still problematic. To rectify this we propose to modify one of the constraints of the non-Abelian theory without altering its canonical Hamiltonian nor the number of physical states.