Twistor diagrams and a quantum field theory
Abstract
This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical viewpoint, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, l990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sumoverstates idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various mass less propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman 'fish' diagrams of phi(sup 4)theory. However it is found that a more rigorous translation for the timelike fish requires new boundaries to be added to the twistor sumoverstates. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.........4O
 Keywords:

 Field Theory (Physics);
 Particle Interactions;
 Quantum Theory;
 Feynman Diagrams;
 Hypotheses;
 Yukawa Potential;
 Thermodynamics and Statistical Physics