By Stetz A.W.

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108) Each kind of particle has its own propagator, but the +i term in the denominator is ubiquitous. The stands for an infinitesimal positive quantity. It’s job is to get the boundary conditions right as you will see in the derivation. 32CHAPTER 2. 1: The complex k0 plane We know that this will be a function of x−y, so we can make the algebra a bit simpler by setting y = 0. Just remember to replace x → x − y at the end of the calculation. 109) are really the same result, though this is far from obvious.

1. Because of conservation of momentum at each vertex, p = k1 − p1 = p2 − k2 . I have also labeled the loop momentum in such as way as to acknowledge this rule. 3) There are three points to be made about this. The first is that the integral over q is ubiquitous whenever there are loops. This is in fact the last of the Feynman rules for this simple scalar field theory. 63 64 CHAPTER 4. 1: The one-loop correction to the propagator. 2: The truncated one-loop diagram. • For every continuous loop there will be one undetermined momentum and an integral over it of the form d4 q .

THE PROBLEM OF SELF INTERACTIONS 51 interacted. ) At this time the particles are free in the sense explained above. It is customary to call such states “in states,” and write them |α, in . The symbol α stands for all the quantum numbers required to completely specify the state. We will be particularly concerned with the momentum. If there are n particles in the initial state, we can write |k1 , k2 , . . , kn , in . 46) It is understood that in calculating with this expression, one uses the physical mass of the particle.

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