Ashtekar Variables and Matter Coupling
General Relativity and Quantum Cosmology
2016-08-31 v1
Abstract
It has been shown for low-spin fields that the use of only the self-dual part of the connection as basic variable does not lead to spurious equations or inconsistencies. We slightly generalize the form of the chiral Lagrangian of half-integer spin fields and express its imaginary part in a simple form. If the imaginary part is non-vanishing, it will lead to spurious equations. As an example, for (Majorana) Rarita-Schwinger fields the equations of motion of the torsion is solved and it is shown that it vanishes owing to the Fierz identity.
Cite
@article{arxiv.gr-qc/9501021,
title = {Ashtekar Variables and Matter Coupling},
author = {M. Tsuda and T. Shirafuji and H. -J. Xie},
journal= {arXiv preprint arXiv:gr-qc/9501021},
year = {2016}
}
Comments
9 pages, latex