Quantum equivalence of O(3) nonlinear sigma model and the CP1 model: A gauge-independent Hamiltonian approach.

We use Dirac's constrained analysis to quantize the O(3) nonlinear [sigma] model and the CP[sup 1] model without using gauge constraints. The equivalence of the models (at the quantum level) is established provided the identification [ital n][sup [ital a]]=[ital Z][sup *][sigma][sup [ital a]Z], [pi][sup [ital a]]=1/2([pi][sigma][sup [ital a]Z]+[ital Z][sup *][sigma][sup [ital a]][pi][sup *]) ([sigma][sup [ital 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.