Basic Twistor Theory, Bi-twistors, and Split-octonions - Roger Penrose скачать в хорошем качестве

Basic Twistor Theory, Bi-twistors, and Split-octonions - Roger Penrose

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. ------------------------------------------------------------------------------------------------------------------------- Join us at https://sites.google.com/view/yrqg/