Abstract
We derive vertex operators in oscillator form as an application of the conserved charges method developed by Vafa for the operator formalism in higher genus Riemann surfaces. This construction proves to be clear, direct and valid for the bosonic and fermionic strings as well as for twisted strings on orbifolds. We discuss the method and construct vertex operators for the bosonic string moving on Z N orbifolds and for the fermionic string in the NSR formulation.
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