Twospinor Formulation of FirstOrder Gravity Coupled to Dirac Fields
Abstract
Twospinor 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 welldefined and may be used in virtually any 4mdimensional manifold with arbitrary signature as well as without any stringent topological requirement on spacetime, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the HilbertEinstein 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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 January 2000
 DOI:
 10.1023/A:1001804718086
 arXiv:
 arXiv:grqc/9903023
 Bibcode:
 2000GReGr..32..145G
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 16 pages, Plain TEX