A note on the covariant anomaly as an equivariant momentum mapping. (English) Zbl 0576.58034
We show that there is a natural gauge invariant presymplectic structure w on the space A of all gauge connections. The covariant axial anomaly \(\bar G\) is found to be the essentially unique infinitesimally equivariant momentum mapping for the action of the group of gauge transformations on (A,w). The infinitesimal equivariance of \(\bar G\) is shown to be equivalent to the Wess-Zumino consistency condition for the consistent axial anomaly G. We also show that the X operator of Bardeen and Zumino, which relates G and \(\bar G,\) corresponds to the one-form (on the space of connections A) of the presymplectic structure w.
MSC:
| 58J90 | Applications of PDEs on manifolds |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
Keywords:
gauge invariant presymplectic structure; gauge connections; covariant axial anomaly; equivariant momentum mappingReferences:
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