Bosonic string quantization in a static gauge

The bosonic string in D-dimensional Minkowski space–time is quantized in a static gauge. It is shown that the system can be described by D − 1 massless free fields constrained on the surface Lm = 0, for m ≠ 0, where Lm are the generators of conformal transformations. The free fields are quantized and the physical states are selected by the conditions Lm|Ψph〉 = 0, for m > 0. The Poincaré group generators on the physical Hilbert space are constructed and the critical dimension D = 26 is recovered from the commutation relations of the boost operators. The equivalence with the covariant quantization is established. A possible generalization to the AdS string dynamics is discussed. (paper)