Self-trapping phenomenon in (2+1)-dimensional quantum electrodynamics and its application to high-T_c cuprates with Neel ordering

The strong coupling effect in the (2+1)-dimensional quantum electrodynamics (QED_3) description of the $S=1/2$ Heisenberg antiferromagnet is studied in terms of a canonical transformation which has been used in the small polaron theory in electron-phonon systems. In the N{\' e}el ordered phase, we show that the Dirac fermions are localized and the spectral function is of the Gaussian form due to the coupling to the longitudinal gauge field. The width of the broad line shape is \sim 4J with J the superexchange interaction energy and the localization length is sim 3a, with a the lattice constant.

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