Gravity in hyperspin manifolds
type: Item
instance of: scholarly article
title: Gravity in hyperspin manifolds
zbMATH Open document ID: 0649.53042
DOI: 10.1007/BF00670753
author: Shlomit Ritz Finkelstein
published in: International Journal of Theoretical Physics
publication date: 1988-01-01T00:00:00Z
review text: The author investigates the dynamics of a Bergmann manifold, i.e. a differentiable manifold of dimension \(n=N\) 2 supporting a bundle of spinor spaces of dimension N, and possessing a mapping \(\sigma\) from its tangent spaces to Hermitian spinor forms. It is shown that every invariant analytic function depending on \(\sigma\) and its first m derivatives can be expressed in terms of the chronometric tensor g and its first m derivatives. Since Bergmann manifolds having dimension \(n>4\) do not admit invariant second order equations for \(\sigma\), the author exhibits a family of invariant actions which lead to nth order quasilinear equations of motion, and reduce to the Einstein-Hilbert action when \(n=2\). These yield gauge particles having the spins 1/2, 1, 3/2, and 2. Contents include: an introduction containing an overview of hyperspin theory; search for actions on Bergmann manifolds; hypergravity; and conclusions.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83D05
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 4060265
zbMATH Keywords: hyperspin
zbMATH Keywords: Bergmann manifold
zbMATH Keywords: spinor spaces
zbMATH Keywords: chronometric tensor
zbMATH Keywords: invariant actions
zbMATH Keywords: hypergravity
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
cites work: Two-Component Spinors in General Relativity
cites work: Hyperspin and Hyperspace
cites work: Hyperspin manifolds
cites work: The Einstein Tensor and Its Generalizations
cites work: Spin-tensorial concomitants of the spin-tensor field
cites work: Q5571644
cites work: Q4756474
full work available at URL: https://doi.org/10.1007/bf00670753
OpenAlex ID: W1994028190
description: scientific article; zbMATH DE number 4060265