A gauge-theoretic description of μ-prolongations, and μ-symmetries of differential equations

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Gaeta, Giuseppe

关键词: Symmetry of differential equations;    Prolongations;    mu-symmetry;    Gauge theories;   

DOI  :  10.1016/j.geomphys.2009.01.004

来源: Elsevier

【 摘 要 】

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 It-prolongation of vector fields (which generalizes the x-prolongation of Muriel and Romero), and hence mu-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free