Abstract: Twistor theory was introduced in the mid 1960s as an approach to
combining quantum theory with space-time structure. A driving
force behind the introduction of Twistor Theory was to combine the
quantum-field theoretic requirement of positive frequency with the
structure of space-time. In order to achieve this, the notion of
twistor space was introduced to codify the structure of space-time in
a way which related it to the splitting of the twistor space into two
halves, one representing positive frequency, and the other
representing negative frequency. Standard twistor theory involves a
complex projective 3-space PT which naturally divides into two
halves PT + and PT – , joined by their common 5-real-dimensional
boundary PN. The points of the space PN represent light rays in
Minkowski space-time. However, this splitting has two quite
different basic physical interpretations, namely positive/negative
helicity and positive/negative frequency, which ought not to be
confused in the formalism, and the notion of “bi-twistors” is
introduced to resolve this issue. It is found that quantized bi-twistors
have a previously unnoticed G 2 * structure, which enables the split-
octonion algebra to be directly formulated in terms of quantized bi-
twistors, once the appropriate complex structure is incorporated.
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