An explicit construction of Wakimoto realizations of current algebras

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra Ĝk can be associated with each parabolic subalgebra P = (G0+G+) of the Lie algebra G, where in the standard case G0 is the Cartan and P is the Borel subalgebra. In this letter we obtain an explicit formula for the Wakimoto realization in the general case. Using Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket realization of the G-valued current in terms of symplectic bosons belonging to G+ and a current belonging to G0. We then quantize the formula by determining the correct normal ordering. We also show that the affine-Sugawara stress-energy tensor takes the expected quadratic form in the constituents.