Constrained current algebras and g/u(1)d conformal field theorie

Operator quantization of the WZNW theory invariant with respect to an affine Lie algebra ĝ with a constrained û(1)d subalgebra is performed using Diracʹs procedure. Upon quantization the initial energy-momentum tensor is replaced by the g/u(1)d coset construction. The sû(2) WZNW theory with a constrained û(1) current is equivalent to the su(2)/u(1) conformal field theory.