Principle of Relativity, 24 possible kinematical algebras and new geometries with Poincaré symmetry

Abstract

From the principle of relativity with two universal invariant parameters $c$ and $l$, 24 possible kinematical (including geometrical and static) algebras can be obtained. Each algebra is of 10 dimensional, generating the symmetry of a 4 dimensional homogeneous space-time or a pure space. In addition to the ordinary Poincaré algebra, there is another Poincaré algebra among the 24 algebras. New 4d geometries with the new Poincaré symmetry are presented. The motion of free particles on one of the new space-times is discussed.

11 pages, talk on the 9th Asia-Pacific International Conference on Gravitation and Astrophysics, Jun. 29-Jul. 2, Wuhan, China

References in corpus (1)

• The Principle of Relativity, Kinematics and Algebraic Relations

Cited by in corpus (1)

• Possible Supersymmetric Kinematics