BRST invariant $C{P}^1$ model through improved Dirac quantization

The Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the $C{P}^1$ model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the $C{P}^1$ model. Exploiting the Hopf bundle, we also show that the $C{P}^1$ model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.