The Lie derivative of spinor fields: theory and applications
| dc.creator | Godina, Marco | |
| dc.creator | Matteucci, Paolo | |
| dc.date | 2005-04-18 | |
| dc.date.accessioned | 2026-07-07T05:19:13Z | |
| dc.date.available | 2026-07-07T05:19:13Z | |
| dc.description | Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these structures admit a canonical decomposition of the pull-back vector bundle i_P^*(TQ) = P\times_Q TQ over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, such a decomposition defines an infinitesimal canonical lift. This lift extends to a prolongation Gamma-structure on P. In this general geometric framework the concept of a Lie derivative of spinor fields is reviewed. On specializing to the case of the Kosmann lift, we recover Kosmann's original definition. We also show that in the case of a reductive G-structure one can introduce a "reductive Lie derivative" with respect to a certain class of generalized infinitesimal automorphisms, and, as an interesting by-product, prove a result due to Bourguignon and Gauduchon in a more general manner. Next, we give a new characterization as well as a generalization of the Killing equation, and propose a geometric reinterpretation of Penrose's Lie derivative of "spinor fields". Finally, we present an important application of the theory of the Lie derivative of spinor fields to the calculus of variations. | |
| dc.description | 28 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0504366 | |
| dc.identifier | http://arxiv.org/abs/math/0504366 | |
| dc.identifier | Int. J. Geom. Methods Mod. Phys. 2 (2005) 159-188 | |
| dc.identifier | doi:10.1142/S0219887805000624 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74939 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53A55, 53C10, 53C27, 58A20 | |
| dc.title | The Lie derivative of spinor fields: theory and applications | |
| dc.type | text |