Nuclear Physics B302 (1988) 81-103 North-Holland, Amsterdam PARTICLES, TWlSTORS AND THE DIVISION ALGEBRAS Ingemar BENGTSSON f The Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2BZ, UK Martin CEDERWALL Laboratoire de Physique Th~orique de l'Ecole Normale Sup~rieure*, France Received 29 June 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 projective 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. 1. Introduction and motivation The physical and mathematical understanding of properties of massless super- symmetric particles and strings moving space-time is from certain aspects quite incoherent. Specifically unsatisfactory is the lack of a manifestly covariant treat- ment at the quantum level. Classically, covariant actions of the superparticle [1] and its string generalization [2] exist and are well understood. The fermionic constraint structure in these theories, however, turns out to be such (mixing first and second class constraints [3] in the same spinor) that conventional quantization procedures fail to maintain manifest Lorentz invariance [4] (a not universally acknowledged statement [5]). One way of dealing with this problem is to add auxiliary "Stiickelberg" degrees of * Supported by the Swedish Natural Science Research Council. On leave of absence from Chalmers University, G~Steborg,Sweden. * Laboratoire Propre du Centre National de la Recherche Scientifique, associ6 & l'Ecole Normale Suprrieure et ~ l'Universit6 de Paris-Sud. Postal address: 24 rue Lhomond, 75231 Paris cedex 05, France. 0550-3213/88/$03.50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)