Continuous translations are broken by an ABJ-like anomaly to a discrete non-Abelian symmetry in a broad class of non-relativistic continuum field theories.
Some topological issues for ferromagnets and fluids
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abstract
We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be defined, but a nonsingular definition of the other moments requires an enlargement of the phase space which illuminates a close relation to fluid mechanics. We also discuss the nontrivial connectivity of the phase space for two and three dimensions and show how this feature can be incorporated in the quantum theory, working out the two-dimensional case in some detail.
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Anomalous Continuous Translations
Continuous translations are broken by an ABJ-like anomaly to a discrete non-Abelian symmetry in a broad class of non-relativistic continuum field theories.