We consider generalized (possibly depending on fields as well as on space–time variables) gauge transformations and gauge symmetries in the context of general – that is, possibly non variational nor covariant – differential equations. In this case the relevant principal bundle admits the first jet bundle (of the phase manifold) as an associated bundle, at difference with standard Yang–Mills theories. We also show how in this context the recently introduced operation of μ-prolongation of vector fields (which generalizes the λ-prolongation of Muriel and Romero), and hence μ-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development.
A gauge-theoretic description of mu-prolongations, and mu-symmetries of differential equations / G. Gaeta. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 59:4(2009), pp. 519-539. [10.1016/j.geomphys.2009.01.004]
A gauge-theoretic description of mu-prolongations, and mu-symmetries of differential equations
G. GaetaPrimo
2009
Abstract
We consider generalized (possibly depending on fields as well as on space–time variables) gauge transformations and gauge symmetries in the context of general – that is, possibly non variational nor covariant – differential equations. In this case the relevant principal bundle admits the first jet bundle (of the phase manifold) as an associated bundle, at difference with standard Yang–Mills theories. We also show how in this context the recently introduced operation of μ-prolongation of vector fields (which generalizes the λ-prolongation of Muriel and Romero), and hence μ-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development.Pubblicazioni consigliate
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