= No-ghost theorem for the critical bosonic string
In flat 26-dimensional <bosonic string theory>, at ordinary nonzero momentum, take <physical string states> satisfying $L_{n>0}|\psi\rangle=0$ and $(L_0-1)|\psi\rangle=0$. The <inner product> restricted to these states is positive semidefinite. Quotienting by physical <null string states> removes the degeneracy; the resulting <Hilbert space> is represented by the 24 transverse <string oscillators>. This is a statement about negative-norm matter states, not about removing the auxiliary <Faddeev-Popov ghosts>. It does not remove the bosonic <tachyon>.
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