The Lanczos potential and Chern-Simons theory

Mark D. Roberts

The Lanczos potential and Chern-Simons theory

General Relativity and Quantum Cosmology 2008-08-13 v1

Authors: Mark D. Roberts

Abstract

A new tensor $D$ is introduced which is constructed from the Lanczos potential and is of the same form as that of the Weyl tensor $C$ expressed in terms of the Lanczos potential except that covariant differentiation is replaced by transvection with a vector $v$ . The new tensor has associated invariants $C\cdot D$ and $D^2$ , the first of these can be interpreted as a Chern-Simons term for Weyl $C^2$ gravity. Both invariants allow various tensors to be constructed and some of the properties of these are investigated by using exact examples.

Keywords

chern-simons theory killing-yano tensors knot invariants

Cite

@article{arxiv.0808.1687,
  title  = {The Lanczos potential and Chern-Simons theory},
  author = {Mark D. Roberts},
  journal= {arXiv preprint arXiv:0808.1687},
  year   = {2008}
}