Two-spinor Formulation of First Order Gravity coupled to Dirac Fields
Abstract
Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any 4m-dimensional manifold with arbitrary signature as well as without any stringent topological requirement on space-time, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the Hilbert-Einstein Lagrangian is second order also when expressed in terms of soldering forms. A covariant splitting is then analysed leading to a first order Lagrangian which is recognized to play a fundamental role in the theory of conserved quantities. The splitting and thence the first order Lagrangian depend on a reference spin connection which is physically interpreted as setting the zero level for conserved quantities. A complete and detailed treatment of conserved quantities is then presented.
Cite
@article{arxiv.gr-qc/9903023,
title = {Two-spinor Formulation of First Order Gravity coupled to Dirac Fields},
author = {Marco Godina and Paolo Matteucci and Lorenzo Fatibene and Mauro Francaviglia},
journal= {arXiv preprint arXiv:gr-qc/9903023},
year = {2008}
}
Comments
16 pages, Plain TEX