Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

An action-angle representation of spin variables is used to relate the large-S Heisenberg antiferromagnet to the O(3) nonlinear sigma model quantum field theory, with precise equivalence for integral S. A variant theory is found for half-integral S. Dynamic mass generation by the Néel magnon is predicted.