QUANTUM EQUIVALENCE OF O(3) NONLINEAR SIGMA-MODEL AND THE CP(1) MODEL - A GAUGE-INDEPENDENT HAMILTONIAN APPROACH

We use Dirac's constrained analysis to quantize the O(3) nonlinear sigma model and the CP1 model without using gauge constraints. The equivalence of the models (at the quantum level) is established provided the identification n(a)=Z*sigma(a)Z, pi(a)=1/2(pisigma(a)Z+Z*sigma(a)pi*) (sigma(a)=Pauli matrices) is used to relate the canonical variables. While the first relation has been discussed in the literature, the second relation connecting the canonical momenta is a new observation. It plays a significant role in displaying the above stated equivalence.