Twistor
The twistor theory is the mathematical theory which maps the geometric objects of the four dimensional space-time (Minkowski space) into the geometric objects in the 4-dimensional complex space with the metric signature (2,2).The coordinates in such a space are called twistors.
For some time there was hope that the twistor theory may be the right approach towards solving quantum gravity, but such hopes did not get to fruition.
The twistor approach appears to be especially natural for the solving the equations of motion of the massless fields of the arbitrary spin.
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