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We present a new approach to the low temperature dynamics of a quantum Heisenberg antiferromagnetic chain, which employs a combination of techniques: exact finite chain calculations; exact Bethe Ansatz calculations; and exact sum rules and selection rules. A striking property of the selection rules is that the contribution of several classes of states to the dynamics in non-zero field for finite systems is shown to vanish in the thermodynamic limit. Many novel quantum field-dependent effects appear such as soft modes, and multiple peak structure in the structure factor, which should be experimentally observable.