# Amplitude of Vertex Diagram: Unchanged?

• noether21
In summary, the amplitude for a vertex diagram remains unchanged when the momenta on the external legs are multiplied by -1 due to crossing symmetry. However, the analytic continuation argument used to derive crossing symmetry may not apply directly when massless particles are involved and the external legs are not all on mass-shell. Further analysis is needed to fully understand the implications of this scenario.

#### noether21

If the momenta on the three external legs p(incoming fermion), p'(outgoing fermion) and
p-p' (photon) of a vertex diagram are replaced by -p, -p' and p'-p respectively (i.e., all the external momenta are multiplied by -1) does the amplitude remain unchanged?

yes due to crossing symmetry

The analytic continuation argument used to derive crossing symmetry (Itzykson & Zuber)
seems to require that there are no massless particles (vacuum is an isolated point). Further
it appears that the external legs must be on mass-shell in the crossing symmetry derivation.
In the 3-point vertex function all the external legs cannot be on mass-shell. I think the
answer to the question is still yes, but short of a lengthy analytic continuation argument
that handles massless particles and doesn't require mass-shell condition (which may not even work), it's unclear how crossing symmetry can be applied directly. Any thoughts?

ah yes, a photon is involved, didn't thought of that =/

## What is the amplitude of a vertex diagram?

The amplitude of a vertex diagram is the maximum displacement or distance from the equilibrium position of the vertex. It represents the maximum energy that the system can possess at any given time.

## How is the amplitude of a vertex diagram calculated?

The amplitude of a vertex diagram can be calculated by measuring the distance from the equilibrium position to the maximum displacement of the vertex.

## What factors affect the amplitude of a vertex diagram?

The amplitude of a vertex diagram is affected by the initial conditions of the system, such as the initial displacement or velocity of the vertex, as well as any external forces acting on the system.

## Does the amplitude of a vertex diagram change over time?

No, the amplitude of a vertex diagram remains constant over time as long as the system is undisturbed and follows a harmonic motion pattern.

## Can the amplitude of a vertex diagram be negative?

Yes, the amplitude of a vertex diagram can be negative if the vertex is displaced in the opposite direction from the equilibrium position. This indicates that the system is undergoing a downward motion.