### Abstract

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra Ĝ_{k} can be associated with each parabolic subalgebra P = (G_{0} + G_{+}) of the Lie algebra G, where in the standard case G_{0} 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 G_{0}. 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.

Original language | English |
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Pages (from-to) | 1999-2011 |

Number of pages | 13 |

Journal | Modern Physics Letters A |

Volume | 11 |

Issue number | 24 |

DOIs | |

Publication status | Published - Jan 1 1996 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Astronomy and Astrophysics
- Physics and Astronomy(all)

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## Cite this

*Modern Physics Letters A*,

*11*(24), 1999-2011. https://doi.org/10.1142/S0217732396001995