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

- 9 ANATOL NOWICKI COMPOSITE SPACETIME FROM TVISTORS AND ITS EXTENSIONS ABSTRACT: The main -ideas of ihe tbjistor and. supertuistor descri.pt ions of spacetime and superspace in D—d and D=ó dimensions are considered briefly from a didactical point of uiew. I/e underline also the role of complex áuiBÍor formalism for D=d and the quaternionic twistor description for D=ő dimensions. 1. Int.roduci.lon. The theory of twistors has been formulated by Eager Penrose CI] in order to unify the quantum mechanical and the spacetime descriptions of Nature. It is well known that quantum mechanics deals with mathematical methods based on the complex structure of a Hilbert space of physical states Cthe probability amplitudes are the complex numbers). On the other hand, the theory of relativity demands the spacetime points to be described by real fourvectors! Cthe coordinates of the spacetime events are the real numbers)

, The difficulties in a consistent formulation of a relativistic quantum theory are immediately related to this fact. The main idea of the twistor theory is to treat the real coordinates of spacetime points as composed quantities of the complex objects so called twistors. Therefore, in the twistor theory the most fundamental objects are the twistors instead of the real spacetime paints. Mathematically twistors are the conformal 0Cd,2) spinors