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
- 14 Minkowski Space or the null twistors for that of the real Minkowski space time. 3. Supersymmetric extension of the Penrose incidence equation. The aim of supersymmetry is to give a unified mathematical description of bosonic and fermionic fields. Therefore, one can consider bosons and fermions using the same theoretical scheme. Supersymmetry allows us to transform the descriptions of bosonic fields into fermionic ones and vice versa. CFor more interested reader in this subject we recommend the references Löí Therefore, in order to have a possibility of the description of bosonic and fermionic fields by using the twistor theory one has to extend it supersymmetrically . The supersymmetry replaces the notation of a space—time point x=Cx°, x 1 , x 2, x 3) by an appropriate £=Cx°, x 1 , x 2, x 3; © K 5> point of the superspace adding N Grassmann variables O , ... , O^,. These additional degrees of freedom anticommute themselves. Now, we can define a supervector representing D— <1 N—extended superspace as follows x = Cx°,x 1 ,x 2 ,x 3; e 4,...,e N> = cx^ ;e A) ciia) where M = 0 4 ; A = 1, ..., N = x^ - = 0 <© A,e B> = e Ae B + e Be A = o . ciib> [x^ej = x^e, - Gx^ = o A A A The commuting coordinates of a supervector are called bosonic ones whereas its anticommuting coordinates are called anticommut ing ones. In the same spirit one can generalize the twistor approach introducing N-extended supertwistors T cn 3=Co a, % %,.. . , e N Cbosonic supertwistors) and the fermionic N—extended supertwistors
