1) Consider the real-valued Klein-Gordon equation of motion: (Ott - V2 + m?) 4 =0 (1) Define the KG propagator (Green operator) as the solution to the inhomogeneous KG equation: (att - V2 + m?) G(x - y) = -i8(x -y) (2) where x and y are 2 points in Minkowski space. The use of i on the right-hand side varies with author to author, and Peskin and Schroeder use it to remove an i that would otherwise appear in the propagator expression. Derive the following: H . G(x - y) = (2 TT ) 4 83 pl (3) R3 where the integral, I, is defined as: e -ip.(x-y) I := / dw R W2 - E- ( 4 ) Remember that the dispersion relation is: EX := p/2 + m? (5) You should be sure to remind yourself of how to take inner products of 4-vectors. This is given very succinctly in Peskin and Schroeder towards the bottom of page xix