Higher-dimensional Riemannian geometry and quaternion and octonion spaces

Journal Article · Wed Feb 01 00:00:00 EST 1984 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526132· OSTI ID:5168682

Moffat, J W

An eight-dimensional Riemannian geometry is shown to be the basis of a nonsymmetric theory of gravitation. A hyperbolic complex structure is imposed and the group structure is GL(8,R)..-->..GL(4,R)xGL(4,R)containsGL(4,R). Octonion and quaternion division algebras are used to represent geometrical quantities and spinors. A Lagrangian is constructed that is related to supersymmetry and supergravity theories. The group structure for a hyperbolic octonion scheme is GL(8,q/sub H/)..-->..GL(4,O/sub H/)approx. =GL(4,q/sub H/) xGL(4,q/sub H/)containsGL(4,q/sub H/), while a simpler scheme based on hyperbolic quaternions is GL(8,C)..-->..GL(4,q/sub H/)approx. =GL(4,C)xGL(4,C)containsGL(4,C).

• Research Organization: Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canada
• OSTI ID: 5168682
• Journal Information: J. Math. Phys. (N.Y.); (United States), Vol. 25:2
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GRAVITATION
RIEMANN SPACE
LAGRANGIAN FUNCTION
MANY-DIMENSIONAL CALCULATIONS
SPINORS
SUPERSYMMETRY
SYMMETRY GROUPS
FUNCTIONS
MATHEMATICAL SPACE
SPACE
SYMMETRY
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation