0 CP 1 model with Hopf interaction : The quantum theory

The CP 1 model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression for the quantum correction to the expectation value of the energy density in the physical sector of this model is derived. The result shows that in the particular operator ordering that we have chosen to work with, the quantum effect has a divergent contribution of O(¯ h 2) in the energy expectation value. But, interestingly the Hopf term, though topological in nature, can have a finite O(¯ h) contribution to energy density in the homotopically nontrivial topological sector. Finally, the extended Lagrangian incorporating the BT auxiliary fields is computed in the conventional framework of BRST formalism exploiting Faddeev-Popov technique of path integral method.