Particles, twistors and the division algebras
Artikel i vetenskaplig tidskrift, 1987

We study twistorial mechanics of particles and super-particles in six dimensions. To this end we formulate (in a general division algebra framework) a twistor theory in D = 6 based on quaternionic numbers, and prove the equivalence between this version of particle dynamics and the ordinary one. The super-twistors define a covariant and gauge invariant concept of a super world-line and allow us to write an action for the supersymmetric particle that is not plagued by the content of second class constraints that prevents a covariant quantization in the space-time picture. The notion and geometry of projectile twistor space, and its connection to Minkowski space, are examined and shown to directly generalize the results in D = 3, 4. Quantization is performed and analytic quaternionic eigenfunctions and integrations are discussed. We also draw some conclusions on the possible generalization to ten dimensions.

Författare

Ingemar Bengtsson

Martin Cederwall

Ämneskategorier

Matematik

Fysik