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

- IS - C N3 . . T = CT7

a , . . . , 77

4; u

1, . . . , u

N) e <C ' , where the quantities are fermionic coordinates and the u

A quantities are the bosonic ones [33 . Let us discuss the case of N=1 i.e supersymmetry briefly. that of the simple Ci) Two linearly independent supertwistors span C2;0) superplane in the superspace C

4*

1, in analogy to eqs.C6a,b) we get CT CiJ-v = ' o

1

1 o

1

2" iZ = K

1 "it "12 3= Ö

1 1 0

2 0 n21 n2 2 0 1 n C12) where Z and Ü are complex matrices of 2x2 type made up of bosonic elements. This can be expressed Cef.eqs.C7)) as follows O o cxi _ = 1

Z a^JT = 1Z <

2 = G

in ß

i rßz >2, On + G^n 11 2 1 „„ + On 12 22 Therefore we obtain the sypersymmetric Penrose relation C7c) in the form extension C12a) of the o a _ = íz ß K = Q

C

tn

f C12b) It means that each T

c

1

3=Co

a,Uß

rsupertwistor corresponds to a Cz,0

a) superspace point. However, it is not the only one possibility of the supersymmetrical generalization of the Penrose relation C7c). ii) Applying three linearly independent supertwistors Tí

1

? '

T2

13 13 c

tw

o bosonic and one fermionic space <C

4'

; 1.