Feynman rules for Yukawa theory

[lefebvre]

Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, and maybe an example of application to decay of fermion?

 

[The_Duck]

Srednicki's QFT book does pseudoscalar Yukawa theory.

maybe an example of application to decay of fermion?

The fermion won't decay in a Yukawa theory because the fermion number is conserved. Unless you have something more than the simplest theory in mind?

 

[lefebvre]

The fermion won't decay in a Yukawa theory because the fermion number is conserved. Unless you have something more than the simplest theory in mind?

OK, I can see that the hamiltonian is: $$H_{I}=g\phi\bar{\psi}\psi+h.c.$$
And I have to use it to fermion decay. Isn't this the simplest Yukawa theory? Does this hermitian conjugate make different?

 

[The_Duck]

OK, I can see that the hamiltonian is: $$H_{I}=g\phi\bar{\psi}\psi+h.c.$$
And I have to use it to fermion decay. Isn't this the simplest Yukawa theory? Does this hermitian conjugate make different?

Are you talking about decay of the $\psi$ particle? There is a U(1) symmetry $\psi \to e^{i \theta} \psi$ under which the Hamiltonian is invariant. This leads to conservation of $\psi$ number. So the $\psi$ particle can't decay. Said another way, in this theory there are no Feynman diagrams you can draw that represent the decay of a $\psi$ particle.