The Lie derivative of spinor fields: theory and applications

Details The Lie derivative of spinor fields: theory and applications The Lie derivative of spinor fields: theory and applications

2005-04-18

arxiv.org/abs/math/0504366v1

Int. J. Geom. Methods Mod. Phys. 2 (2005) 159-188

Mathematics

Differential Geometry

28 pages, 1 figure

Scientific paper

10.1142/S0219887805000624

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.

Affiliated with

Also associated with

No associations

Rating

The Lie derivative of spinor fields: theory and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Lie derivative of spinor fields: theory and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Lie derivative of spinor fields: theory and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-138112