List of Figures

View Image Figure 1:
The Feynman propagator and three- and four-point vertices in Einstein gravity.
View Image Figure 2:
Sample gravity tree-level Feynman diagrams. The lines represent any particles in a gravity theory.
View Image Figure 3:
Sample loop-level Feynman diagrams. Each additional loop represents an extra power of Planck’s constant.
View Image Figure 4:
An example of a five-loop diagram.
View Image Figure 5:
String theory suggests that the three-graviton vertex can be expressed in terms of products of three-gluon vertices.
View Image Figure 6:
The color-ordered gauge theory Feynman rules for obtaining tree-level scattering amplitudes for gravity coupled to matter, via the KLT equations. The Greek indices are space-time ones and the Latin ones are group theory ones. The curly lines are vectors, dotted ones scalars, and the solid ones fermions.
View Image Figure 7:
The three color-ordered Feynman diagrams contributing to the QCD partial amplitude in Eq. (15View Equation).
View Image Figure 8:
As two momenta become collinear a gravity amplitude develops a phase singularity that can be detected by rotating the two momenta around the axis formed by their sum.
View Image Figure 9:
The two-particle cut at one loop in the channel carrying momentum k1 + k2. The blobs represent tree amplitudes.
View Image Figure 10:
Two examples of generalized cuts. Double two-particle cuts of a two-loop amplitude are shown. This separates the amplitude into a product of three tree amplitudes, integrated over loop momenta. The dashed lines represent the cuts.
View Image Figure 11:
The one-loop box integral. Each internal line in the box corresponds to one of the four Feynman propagators in Eq. (51View Equation).
View Image Figure 12:
The planar and non-planar scalar integrals, appearing in the two-loop N = 8 amplitudes. Each internal line represents a scalar propagator.
View Image Figure 13:
Starting from an l-loop planar diagram representing an integral function, an extra line may be added to the inside using this rule. The two lines on the left represent two lines in some l-loop diagram.