Twistor theory: An approach to the quantisation of fields and spacetime
Abstract
Twistor theory offers a new approach, starting with conformallyinvariant concepts, to the synthesis of quantum theory and relativity. Twistors for flat spacetime are the SU(2,2) spinors of the twofold covering group O(2,4) of the conformal group. They describe the momentum and angular momentum structre of zerorestmass particles. Spacetime points arise as secondary concepts corresponding to linear sets in twistor space. They, rather than the null cones, should become “smeared out” on passage to a quantised gravitational theory. Twistors are represented here in twocomponent spinor terms. Zerorestmass fields are described by holomorphic functions on twistor space, on which there is a natural canonical structure leading to a natural choice of canonical quantum operators. The generalisation to curved space can be accomplished in three ways; i) local twistors, a conformally invariant calculus, ii) global twistors, and iii) asymptotic twistors which provide the framework for an Smatrix approach in asymptotically flat spacetimes. A Hamiltonian scattering theory of global twistors is used to calculate scattering crosssections. This leads to twistor analogues of Feynman graphs for the treatment of massless quantum electrodynamics. The recent development of methods for dealing with massive (conformal symmetry breaking) sources and fields is briefly reviewed.
 Publication:

Physics Reports
 Pub Date:
 February 1973
 DOI:
 10.1016/03701573(73)900082
 Bibcode:
 1973PhR.....6..241P