On the classification of the low energy excitations in the doped antiferromagnet

A long-wavelength, low energy hamiltonian is derived to describe the dynamic of a single hole in a quantum antiferromagnet in two or higher spatial dimensions. In this exactly solvable limit a new kind of symmetry is important to classify the elementary spin excitations of a single hole in the t - J model. This symmetry is hidden at finite size or at short wavelength. The resulting classification has important consequences for understanding the physics of doped antiferromagnets. Fermi liquid like s = 1/2 and charge one excitations are still well defined in a quantum antiferromagnet, but are not a complete set to describe the low energy physics.