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An operator formalism for bosonic $\beta-\gamma$ systems on arbitraryalgebraic curves is introduced. The classical degrees of freedom are identifiedand their commutation relations are postulated. The explicit realization of thealgebra formed by the fields is given in a Hilbert space equipped with abilinear form. The construction is based on the "gaussian" representation for$\beta-\gamma$ systems on the complex sphere [Alvarez-Gaum\' e et al, Nucl.Phys. B 311 (1988) 333]. Detailed computations are provided for the two andfour points correlation functions.Comment: 26 pages, plain TeX + harvma

Operator formalism for bosonic beta–gamma fields on general algebraic curves