First Quantization

As we have already discussed in the previous chapter, the classical bosonic string action is invariant under diffeomorphisms or reparametrizations of the world-sheet and conformal rescalings of the intrinsic metric on the world-sheet. Since the process of first quantizing this string is equivalent to second quantizing a point particle theory on the world-sheet that possesses gauge symmetries, then we can expect to encounter the same kinds of difficulties in carrying out the quantization as we did with point particle gauge theories in earlier chapters. We can also expect that the

same methods and techniques developed for point particle field theories to overcome these difficulties may also be applied to strings.