The low energy photoemission spectra in quantum antiferromagnets are s
tudied by using several approximation-free calculations and rigorous t
heorems. The important and measurable property found is that the hole
eigenstates with momenta differing by the antiferromagnetic wave vecto
r Q are equivalent and degenerate in energy. However, the correspondin
g eigenstates differ by the presence or the absence of a well-defined
quasiparticle corresponding to a singular. zero-energy, magnon, carryi
ng spin one and momentum Q. This difference between the two eigenstate
s affects dramatically the spectral weight as a function of the scatte
red momentum, since a sharp effect at the surface of the magnetic Bril
louin zone is predicted, in apparent agreement with recent experimenta
l data.