- #1

Sonny Liston

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## Homework Statement

I'm working with the Yukawa theory, where the interaction term in the Lagrangian density is [itex]g\varphi\overline{\psi}\psi[/itex]. As an exercise for getting used to using the Feynman rules for the theory, I'm asked to show explicitly (i.e. I'm not allowed to invoke charge conservation) that, at tree level, the amplitude for the process [itex]e^-\varphi \rightarrow e^+\varphi[/itex] is zero.

## Homework Equations

The interaction is [itex]g\varphi\overline{\psi}\psi[/itex]. Just set notation, we're using Srednicki's QFT book and the discussion of Feynman rules for the Yukawa theory is chapter 45.

## The Attempt at a Solution

This process yields two diagrams at tree level. My first though was that I would write down the diagrams and they would cancel in some nice way, but I'm actually stuck even trying to write down sensible diagrams for this process; writing down diagrams that are in accord with the Feynman rules while also yielding things that look like amplitudes is proving difficult. In particular, there are no barred spinors in the resultant amplitudes; the incoming electron and outgoing positron both contribute unbarred spinors. Is there a way to write down diagrams for this process that make sense? If so, am I on the right track in expecting that they would cancel, or have I totally misunderstood how to go about this?