By Stetz A.W.
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Kn , in . 46) It is understood that in calculating with this expression, one uses the physical mass of the particle. In the same way, one defines “out states” β, out|, “out fields” ϕout (x), and “out” creation operators a†out (k) corresponding to the limit t → ∞. A scattering experiment can be idealized as follows. The initial target and beam particles are prepared so that they are in a unique eigenstate of all the relevant operators. We call this state |α, in . The detectors of the scattered particles are so refined that they can specify that the final state was in the exact eigenstate β, out|.
In addition to the external lines that begin or terminate at a vertex, there will be lines that connect two vertices. These are called internal lines. • Label all lines with their momentum. External lines carry the momentum that is observed in the lab; in the previous example, k1 , k2 , p1 , and p2 . Label the internal lines as you wish, perhaps q1 , q2 , q3 · · · would be a good choice. Put an arrow on each of the internal lines indicating the flow of momentum. The direction you choose will be arbitrary, but you must make a choice.
97) with an additional parameter α that we can tweak at our pleasure. V. Jose and E. J. 1 for a derivation of this rather non-trivial result. 7 See Paul Teller, An Interpretive Introduction to Quantum Field Theory, Chapter 4, for a careful discussion of this point. 6. 104) This is not zero (because of the ω in the denominator) unless |α| = 1. Relativity and causality together require an equal admixture of negativeand positive-energy states. This argument takes on additional significance when spin is taken into account.
A very short introduction to quantum field theory by Stetz A.W.