Loops and trees

Understand

We investigate relations between loop and tree amplitudes in quantum field theory that involve putting on-shell some loop propagators.

• This generalizes the so-called Feynman tree theorem which is satisfied at 1-loop.
• Exploiting retarded boundary conditions, we give a generalization to L-loop expressing the loops as integrals over the on-shell phase space of exactly L particles.
• We argue that the corresponding integrand for L>2 does not involve the forward limit of any physical tree amplitude, except in planar gauge theories.