# Feynman rules for Yukawa theory

• lefebvre
In summary, the conversation discusses the search for a complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, as well as an example of application to fermion decay. Srednicki's QFT book is mentioned as a resource for pseudo-scalar Yukawa theory, but it is noted that fermion decay is not possible in the simplest Yukawa theory due to the conservation of fermion number. The conversation also touches on the invariance of the Hamiltonian under a U(1) symmetry and the absence of Feynman diagrams for fermion decay in this 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?

Srednicki's QFT book does pseudoscalar Yukawa theory.

lefebvre said:
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?

The_Duck said:
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?

lefebvre said:
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.

## 1. What is the Yukawa theory?

The Yukawa theory is a quantum field theory that describes the interactions between particles that have different masses. It was proposed by Japanese physicist Hideki Yukawa in the 1930s and is an important component of the Standard Model of particle physics.

## 2. What are Feynman rules?

Feynman rules are a set of mathematical rules used to calculate the probability of particle interactions in quantum field theory. They were developed by physicist Richard Feynman in the 1940s and are based on the Feynman diagrams that represent particle interactions.

## 3. How do the Feynman rules apply to Yukawa theory?

In Yukawa theory, the Feynman rules are used to calculate the scattering amplitudes of particles with different masses. These rules involve assigning momentum and spin values to each particle in the interaction and then using mathematical equations to determine the probability of the interaction occurring.

## 4. What is the significance of the Yukawa coupling in Feynman rules for Yukawa theory?

The Yukawa coupling is a term in the Feynman rules for Yukawa theory that represents the strength of the interaction between particles with different masses. It is an important parameter that affects the overall behavior and predictions of the theory.

## 5. How are Feynman rules for Yukawa theory used in practical applications?

Feynman rules for Yukawa theory are used in various practical applications, such as in the calculation of particle scattering amplitudes and the prediction of particle properties. They are also used in particle accelerators to study the behavior of particles and in the development of new theories and models in particle physics.

Replies
33
Views
4K
Replies
4
Views
1K
Replies
134
Views
8K
Replies
1
Views
2K
Replies
7
Views
2K
Replies
4
Views
2K
Replies
1
Views
902
Replies
1
Views
1K
Replies
4
Views
2K
Replies
6
Views
1K