Noncanonical groups of transformations, anomalies, and cohomology

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Abstract
Two cohomology classes associated to groups of transformations (symplectic or not) of Hamiltonian and Lagrangian systems are studied. A geometrical interpretation of the family of cocycles arising from a class of nonsymplectic actions is given in terms of the Poisson structure of the phase space of the system. These ideas are used to study nongauge (i.e., anomalous) groups of transformations of (locally or globally defined) Lagrangian systems. In particular, well-known results about the magnetic monopole system are described in this context and some hints relating Yang–Mills anomalies with nonsymplectic groups of transformations are given.

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