Some Spinor-Curvature Identities
James M. Nester, Roh Suan Tung, Vadim V. Zhytnikov
TL;DR
This paper introduces a class of identities linking spinor derivatives and curvature in Riemannian and Riemann-Cartan geometries, with potential applications in General Relativity, especially in 3 and 4 dimensions.
Contribution
It presents new spinor-curvature identities applicable to Riemannian and Riemann-Cartan geometries, including special cases relevant to General Relativity.
Findings
Identifies identities relating quadratic spinor derivatives to linear curvature expressions.
Highlights special cases in 3 and 4 dimensions useful for gravitational theories.
Provides mathematical tools potentially applicable to Einstein's equations and related fields.
Abstract
We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.
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