S-Matrix Theory (ref. 11)

S-Matrix Theory (ref. 11)

1. Standard definition: Giving the Lagrangian from some fields, compute the correlation function of operators, insert that the various points in Space-Time, then compute this object, and take a Fourier transform, using general arguments in quantum field theory you can argue that this object must have poles where particles become one shell, and then compute the multi-residue

   • Assumes presence of poles, formally proven for massive particles, but you can assume true for massless particles too
   • Fourier Transform: Multiply by wave plane wave functions for particles that are incoming, and particles that are outgoing
   • The Standard definition of the S-Matrix computes it as a sum over all possible interactions that can occur in the interior of our Minkowski space-time

2. Quantum Field Theory

   • Feynman diagrams lead to expressions where locality and unitarity are manifest as they come from the explicitly local interactions of the theory
     • Parke and Taylor (80s) - Scattering amplitudes are much simpler
       • Could this mean manifest locality and unitarity are not the basic properties of formation of the S-Matrix

3. Constraints

   • It has to be Poincare covariant
     • Transformations must be consistent with those of asymptotic one-particle states which are irreps. of Poincare
   • Poincare and Weinberg soft theorems