Bosonic String Quantization in Static Gauge

TL;DR

This paper quantizes the bosonic string in static gauge, demonstrating its equivalence to covariant quantization, deriving the critical dimension, and discussing potential extensions to AdS string dynamics.

Contribution

It provides a novel static gauge quantization approach for bosonic strings, establishing the critical dimension and equivalence with covariant methods.

Findings

Critical dimension D=26 is derived from boost operator commutations.

The system reduces to D-1 massless free fields constrained by L_m=0.

The quantization method aligns with covariant quantization results.

Abstract

The bosonic string in D dimensional Minkowski space-time is quantized in static gauge. It is shown that the system can be described by D-1 massless free fields constrained on the surface L_m = 0, for m \neq 0, where L_m are the generators of conformal transformations. The free fields are quantized and the physical states are selected by the conditions L_m|phys>=0, for m>0. The Poincar\'e 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.