![]() ![]() ![]() Tree-level gluon scattering scattering amplitudes are expressed as integrals over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map related to the helicity configuration of the external gluons. These backgrounds are chiral, asymptotically flat gauge fields characterised by their free radiative data, and their underlying integrability is captured by twistor theory. We present all-multiplicity formulae, derived from first principles in the MHV sector and motivated by twistor string theory for general helicities, for the tree-level S-matrix of gluon scattering on self-dual radiative backgrounds. We should then in principle be able to make as much analytic progress in scattering calculations as in the background field case, as G φ and hence the external leg wavefunctions can be written down exactly the propagator (34) for a plane wave background. Assume that both the initial and final coherent states are plane waves depending on n.x for n 2 = 0. There are some conceptual issues to be addressed here, which are best illustrated by example. Applying LSZ amputation (analogous to (18) and (19) but without the additional terms) to external G φ lines gives the asymptotic particle wavefunctions. ![]() 1 except that the background field in the matter propagator is complex. 4 and are precisely as for the usual Furry picture in Fig. The Feynman rules are illustrated in Fig. In this approach particles propagate in the complex background field A D while the interaction (the three-point vertex) between the matter field and the quantised photon field is treated in perturbation theory as usual. G φ can be found explicitly then the coupling to both the initial and final coherent states can be treated without approximation. ![]()
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