GEOMETRIC-QUANTIZATION OF STRINGS AND REPARAMETRIZATION INVARIANCE

The structure of the phase space of closed bosonic strings in R(d-1), 1 and its geometric quantization are investigated. It is shown that the critical dimension d = 26 for bosonic strings arises as a condition of integrability of the quantum connection on the fibers of a bundle of complex structures over a loop space. The connection with BRST (Becchi-Rouet-Stora-Tyutin) string quantization is considered.