Gravity in hyperspin manifolds

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:5644242

Finkelstein, S R

A spin vector sigma/sub AA//sup a/ maps the Hermitian bilinear forms psi/sub (AA)/ to the tangent space dx/sup a/ of time-space manifold at each point x/sup t/ of the manifold. The dimension of the emerging non-Riemannian manifold is n = N/sup 2/. We week the dynamics of that Bergmann manifold. We prove that even though the spin-vector sigma is the fundamental variable of the theory, every invariant analytic function depending on sigma and its first m derivatives alone can be expressed in terms of the chronometric tensor g and its first m derivatives. We prove that invariant actions for Riemannian manifolds of higher dimensions which lead to second order equations of motion (Lovelock and Zumino actions) cannot be generalized to actions for Bergmann manifolds of dimension n = 4 with second order equations. We find a family of actions which lead to Nth order quasilinear equations of motion on Bergmann manifolds and reduce to the Einstein-Hilbert action for N = 2. The resulting gauge particles have at most spin 0, 1/2, 1, 3/2, and 2. We purpose some questions for future study.

• Research Organization: Georgia Inst. of Tech., Atlanta (USA)
• OSTI ID: 5644242
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACTION INTEGRAL
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
GRAVITATION
INTEGRALS
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
RIEMANN SPACE
SPACE
SPIN