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Centre for Particle Theory

Amplitudes

8 Lectures Prof. P. Mansfield

Scattering amplitudes are the basic quantities that we need to compute to be able to predict the outcome of scattering experiments. Feynman diagrams provide an intuitive understanding of their structure but are exceedingly cumbersome to calculate with. Often there can be many cancellations between the diagrams that contribute to any given amplitude, resulting in simple final expressions. Understanding the mathematics that underlies this simplicity has recently led to remarkable advances in our ability to compute the amplitudes themselves. The course aims to provide an introduction to these techniques.

Outline of the course

Spinor variables: massless Dirac equation, dotted and undotted indices, helicity, conjugation, spinor products
Gauge theories: polarization vectors and spinors, helicity, self-duality, LSZ, gauge fixing, colour ordering, fermions
Gauge invariance and tree amplitudes: 3-point, 4-point, n-point all+, n-point one
BCFW in general, and applied to MHV amplitudes
N=4 Super-Yang-Mills amplitudes, Gravity amplitudes (If time permits)

Books for the course

Herbi K. Dreiner, Howard E. Haber and Stephen P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, hep-ph/0812.1594
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B72 (1974) 461-473
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602, hep-th/0501052
Lars Brink, John H. Schwarz, J. Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys. B121 (1977) 77-92
Edward Witten, Perturbative Gauge Theory As A String Theory In Twistor Space, hep-th/0312171