Gravity in hyperspin manifolds
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.
scientific article; zbMATH DE number 4060265