Theory of quantum electrodynamics in three spatial-time dimensions 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 bandwidth, which suggests that the system is in the strong coupling regime with respect to the gauge field interaction describing the phase fluctuations about the pi-flux state.