Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1990. Sectio Physicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 20)

Anatol Nowicki: Composite spacetime from twistors and its extensions

CT In analogy to (12) we have CID TC1) l*tlK _ 1 12 o o P 22 o CO P "ll "12 nli n!2 rj s

1 u 16 iz

1

1 iz 12 0 iz

a

i iz 22 e 1 0 0 0 1 0 0 0 i u where the fermionic supertwistor includes the four C13) fermionic (p

1

, p

2

, ri

i , r/

2) components and also one bosonic u. The (2;1) — superplane is parametrized by a (Z,ö) matrix of 2x3 type with elements satisfying the following incidence relations: (14a) o

a — + (bosonic incidence equation) p

a — iz

ct,f

377

b + 0"u (fermionic incidence equation) (14b) These equations give us a different generalization of the Penrose relation from (12b). Therefore, for N=1 supersymmetry there are two

. possible extensions of Penrose's relation. In case of the N—extended supersymmetry one can genaralize the equation (7c) in N+l different ways. The case

1 of arbitrary N is considered in ref. t33. 4. Quaternionic extension of Penrose's incidence equation for Ond spacetime. There are two possible appraches to D=6 twistor formalism: (i) by extending Penrose's relation from D=4 to D=6 as it has been done by Hungston and Shaw in ref. £4 3. (ii) by replacement of the complex 2x2 matrix Z. In this approach the quaternionic 2x2 matrix i

5? describes sixdimensional (D=ö) real Minkowski spacetime point. One can show that these two approaches are equivalent for the