Maraner, P. and Pachos, J.K. (2008) Universal features of dimensional reduction schemes from general covariance breaking. Annals of Physics, 323 (8). pp. 2044-2072. ISSN 0003-4916
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors.
|Copyright, Publisher and Additional Information:||© 2008 Elsevier Inc. This is an author produced version of a paper published in Annals of Physics. Uploaded in accordance with the publisher's self archiving policy.|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)|
|Depositing User:||Sherpa Assistant|
|Date Deposited:||24 Jul 2008 14:52|
|Last Modified:||08 Jun 2014 22:12|