English

Non-relativistic limit of Einstein-Cartan-Dirac equations

General Relativity and Quantum Cosmology 2018-11-21 v3 High Energy Physics - Theory Quantum Physics

Abstract

We derive the Schr\"{o}dinger-Newton equation as the non-relativistic limit of the Einstein-Dirac equations. Our analysis relaxes the assumption of spherical symmetry, made in earlier work in the literature, while deriving this limit. Since the spin of the Dirac field couples naturally to torsion, we generalize our analysis to the Einstein Cartan-Dirac (ECD) equations, again recovering the Schr\"{o}dinger-Newton equation.

Keywords

Cite

@article{arxiv.1804.04434,
  title  = {Non-relativistic limit of Einstein-Cartan-Dirac equations},
  author = {Swanand Khanapurkar and Arnab Pradhan and Vedant Dhruv and Tejinder P. Singh},
  journal= {arXiv preprint arXiv:1804.04434},
  year   = {2018}
}

Comments

V3: 22 pages, typos and language corrected, clarifying paragraphs added, references added, accepted for publication in Phys. Rev. D