# Calculating Weak Interaction Processes: Four Fermion Invariants in Fermi-Theory

• evilcman
In summary, the conversation discusses the calculation of weak interaction processes using the Fermi-theory. It explores the possibility of Lorentz-scalars being a linear combination of vector*vector and axialvector*axialvector parts, suggesting that axialvector*vector parts should equal zero. However, one person raises confusion about this theory not making sense if a=b=c=d. Another person clarifies that an A*V (axialvector*vector) piece is necessary for the weak interaction to violate parity and acknowledges the mistake.

#### evilcman

In calculations of weak interaction processes in the Fermi-theory,
there are some amplitudes of the form:
$$\bar{a}(\gamma_{\alpha} + \lambda \gamma_{\alpha}\gamma_{5}) b \bar{c}(\gamma^{\alpha} + \gamma^{\alpha}\gamma_5)d$$
where a,b,c,d are Dirac-spinors. Now, if this is a Lorentz-scalar. In that case
it should be a linear combination of a vector*vector and axialvector*axialvector parts,
meaning that axialvector*vector parts should give zero, that is:
$$\bar{a}\gamma_{\alpha}\gamma_{5} b \bar{c}\gamma^{\alpha}d = 0$$
should hold. Can someone show this?

In fact I am a bit confused since $$\gamma_5 \gamma_{\alpha} \gamma^{\alpha} = 4 \gamma_5$$, so if i take for example a=b=c=d, that thing
does not seem to vanish, which does not make sense to me.

You need an A*V piece if you want the weak interaction to violate parity.

## 1. What are four fermion invariants?

Four fermion invariants are mathematical expressions that describe the interactions between four fermions, which are particles that have half-integer spin and follow Fermi-Dirac statistics.

## 2. What is the significance of four fermion invariants in physics?

Four fermion invariants play a crucial role in the Standard Model of particle physics, as they are used to describe the strong and weak nuclear forces between elementary particles.

## 3. How are four fermion invariants calculated?

Four fermion invariants are calculated using Feynman diagrams, which are graphical representations of particle interactions. These calculations involve considering all possible ways that four fermions can interact and summing them together.

## 4. Can four fermion invariants be used to predict particle behavior?

Yes, four fermion invariants can be used to make predictions about the behavior of particles in various physical processes. They have been successfully used to predict the outcomes of high-energy particle collisions at accelerators such as the Large Hadron Collider.

## 5. Are four fermion invariants a fundamental part of nature?

Four fermion invariants are not considered to be fundamental in the same way that particles and forces are. They are a mathematical construct that is used to describe and understand the behavior of particles, but they are not considered to be a fundamental part of nature like the laws of physics.