Abstract The formalism of twistors provides a new approach to the description of basic physics. The points of Minkowski space-time are represented by 2-dimensional linear subspaces of a complex 4-dimensional vector space (flat twistor space) on which a Hermitian form of signature ++-- is defined. Free massless fields can be represented in terms of the sheaf cohomology of portions of this space. Twistor space (or a suitable part of it) can be expressed in two different ways as a complex fibration. If one or the other fibration structure is deformed, the resulting space represents not empty Minkowski space but, in one case, the general “right-flat” solution of Einstein's vacuum equations and, in the other, the general (left-handed) solution of Maxwell's equations. These provide the most primitive types of interaction (gravitational or electromagnetic) which may generalize to other fields in a comprehensive twistor scheme for the description of elementary particles.
[1]
R. Penrose,et al.
Twistor theory: An approach to the quantisation of fields and space-time
,
1973
.
[2]
E. Newman.
Heaven and its properties
,
1976
.
[3]
Roger Penrose,et al.
The apparent shape of a relativistically moving sphere
,
1959,
Mathematical Proceedings of the Cambridge Philosophical Society.
[4]
R. Penrose.
Twistor quantisation and curved space-time
,
1968
.
[5]
Roger Penrose,et al.
Solutions of the Zero-Rest-Mass Equations
,
1969
.
[6]
R. Penrose.
Nonlinear gravitons and curved twistor theory
,
1976
.
[7]
Anatolii A. Logunov,et al.
Analytic functions of several complex variables
,
1965
.
[8]
R. Penrose.
The nonlinear graviton
,
1976
.