Covariant quantization of string based on BRS invariance

Abstract

Covariant canonical quantization of the bosonic string is performed, based on the BRS invariance principle. Defining a physical state by a modified form of Kugo-Ojima's subsidiary condition Q B|phys〉 = 0 ( Q B = BRS charge), we prove a no-ghost theorem in a simple manner. There an interesting relation between critical dimension and BRS symmetry is noticed; namely, the conditions D = 26 and α 0 = 1 for the space-time dimension D and the zero-intercept α 0 of leading trajectory are required by the nilpotency Q B 2 = 0 of the BRS charge. In addition, ghost number fractionization is observed in this system.