Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-11-17
Mod.Phys.Lett. A21 (2006) 265-274
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, no figures, to appear in Mod. Phys. Lett. A
Scientific paper
10.1142/S0217732306019396
In this work we deal with the extension of the Kaluza-Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce fields equations and gauge transformations in the four-dimensional picture. More precisely, in fields equations any dependence on extra-coordinates is canceled out by an integration, as consequence of the unobservability of extra-dimensions. Thus, by virtue of this extra-dimensions unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein-Yang-Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang-Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.
Cianfrani Francesco
Montani Giovanni
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