# Scattering Amplitudes in Gauge Theory and Gravity by Henriette Elvang

By Henriette Elvang

Delivering a accomplished, pedagogical creation to scattering amplitudes in gauge concept and gravity, this publication is perfect for graduate scholars and researchers. It deals a gentle transition from easy wisdom of quantum box thought to the frontier of contemporary learn. development on easy quantum box thought, the booklet begins with an advent to the spinor helicity formalism within the context of Feynman ideas for tree-level amplitudes. the cloth lined comprises on-shell recursion kinfolk, superamplitudes, symmetries of N=4 great Yang-Mills thought, twistors and momentum twistors, Grassmannians, and polytopes. The presentation additionally covers amplitudes in perturbative supergravity, 3D Chern-Simons subject theories, and color-kinematics duality and its connection to 'gravity=(gauge theory)x(gauge theory)'. simple wisdom of Feynman principles in scalar box thought and quantum electrodynamics is thought, yet all different instruments are brought as wanted. labored examples display the options mentioned, and over one hundred fifty routines support readers soak up and grasp the fabric.

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**Scattering Amplitudes in Gauge Theory and Gravity**

Offering a accomplished, pedagogical creation to scattering amplitudes in gauge idea and gravity, this publication is perfect for graduate scholars and researchers. It deals a gentle transition from easy wisdom of quantum box concept to the frontier of contemporary examine. development on simple quantum box conception, the ebook begins with an creation to the spinor helicity formalism within the context of Feynman principles for tree-level amplitudes.

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**Extra resources for Scattering Amplitudes in Gauge Theory and Gravity**

**Example text**

N] + · · · + An [23 . . 1 n] = 0 . 85) 8 This can be seen by direct counting, but see also the analysis in [6]. 5 Yang–Mills theory, QCD, and color-ordering 35 The vanishing of this sum of n − 1 color-ordered amplitudes is also called the photon decoupling identity; it follows from taking one of the generators T a proportional to the identity matrix. 85) holds for n = 4 for the case where gluons 1 and 2 have negative helicity and 3 and 4 have positive helicity. 86) σ ∈OP({α},{β T }) where {β T } denotes the reverse ordering of the labels {β} and the sum is over ordered permutations “OP,” namely permutations of the labels in the joined set {α} ∪ {β T } such that the ordering within {α} and {β T } is preserved.

Square spinors: reality conditions. The spinor field is the Dirac conjugate of . e. the components of p μ are real numbers. Thus for real momenta p μ real : [ p|a = (| p a˙ )∗ and p|a˙ = (| p]a )∗ . 1 It may not seem physical to take p μ complex, but it is a very very very useful strategy. We will see this repeatedly. 1 One can keep p μ real and change the spacetime signature to (−, +, −, +); in that case, the angle and square spinors are real and independent. Spinor helicity formalism 18 Spinor completeness relation.

T an )i j . If we want to study the interactions of gluons with their supersymmetric partners, the gluinos, then the fermion field must transform in the adjoint so we replace with λ = λa T a and include a trace in the Lagrangian. The trace-structure for gluon–gluino scattering is exactly the same as for gluon scattering. We have by now seen enough examples of how to use spinor helicity formalism in the context of standard Feynman rules. It is about time that we get a little fancier. Therefore we postpone further discussion of Yang–Mills and super Yang–Mills amplitudes until we have developed a few more tools.