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

Abstract

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 {\em exactly solvable} limit a {\em 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 {\em complete} set to describe the low energy physics.