Null string state

A null string state is both physical and spurious. It has zero norm and is quotiented from the physical state space.

The physical state space of old covariant quantization is quotiented by its physical spurious states, which are orthogonal to all physical states. In a ghost-free sector these form the radical of the semidefinite inner product. The quotient retains positive physical polarizations.

For $L_0|p⟩=-|p⟩$, the descendant $Z=(L_{-2}+\frac{3}{2}{L}_{-1}^2)|p⟩$ obeys $L_{1}Z=0$ and $L_{2}Z=(D-26)|p⟩/2$. It becomes physical and null at 26 and supplies the scalar quotient needed for the massive spin-two light-cone gauge in string theory spectrum.