Physics / research
On-shell structures and scattering amplitudes
Use on-shell variables, factorization, recursion, and unitarity to compute scattering amplitudes while exposing the assumptions of each construction.
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Module 01 research
On-shell structures and scattering amplitudes
Use on-shell variables, factorization, recursion, and unitarity to compute scattering amplitudes while exposing the assumptions of each construction.
- 01
Spinor-helicity variables for massless momenta
Factor null momentum matrices into spinors with explicit metric, bracket, energy-sign, and crossing conventions.
31 min - 02
Little-group scaling and three-point amplitudes
Solve helicity-weight constraints on analytic three-point functions and explain why real massless three-particle kinematics is insufficient.
31 min - 03
Color ordering and partial amplitudes
Separate color tensors from ordered kinematics and identify the cyclic adjacency restrictions on tree poles.
30 min - 04
BCFW complex shifts and boundary terms
Preserve nullness and momentum conservation under a complex shift and retain the contour contribution at infinity unless it is justified to vanish.
32 min - 05
Tree-amplitude factorization tests
Check pole residues, internal-state phases and ordered channels while recognizing the contact information factorization cannot fix.
31 min - 06
Generalized unitarity and integral coefficients
Match cut residues to a declared loop-integral basis and identify rational, dimensional, and regularization information that four-dimensional cuts can miss.
33 min - 07
Soft theorems and universal limits
Calculate a leading color-ordered soft factor with explicit momentum scaling and distinguish amplitude singularities from regulated observables.
31 min - 08
Collinear splitting amplitudes
Separate helicity-level splitting factors from color- and spin-summed kernels and state the time-like collinear and infrared assumptions.
32 min - 09
Color-kinematics duality and double copy
Check Jacobi-compatible numerator representations and the color-to-kinematics replacement without mistaking arbitrary squares for pure-gravity amplitudes.
34 min - 10
Amplitude-bootstrap assumptions and open problems
State the function space and physical constraints of a bootstrap, expose contact-term null directions, and bound claims of uniqueness or completion.
34 min