  Theory of quantum electrodynamics in three spatial-time dimension is applied
to the two-dimensional $S=1/2$ quantum Heisenberg antiferromagnet in order to
investigate a doped hole in high-temperature superconductors. Strong coupling
analysis of the U(1) gauge field interaction is carried out to describe
spectral broadening observed in the undoped compounds. It is found that the
fermionic quasiparticle spectrum is of Gaussian form with the width about 3J,
with J being the superexchange interaction energy. The energy shift of the
spectrum is on the order of the quasiparticle band width, which suggests that
the system is in the strong coupling regime with respect to the gauge field
interaction describing the phase fluctuations about the staggered flux state.
