- #1

rwooduk

- 762

- 59

## Homework Statement

## Homework Equations

Please see below.

## The Attempt at a Solution

No idea about part (a).

Trying to work out part (b), I asked my tutor and he said:

The derivation is the one where we assume the Dirac equation is invariant under local gauge transformations.

I think it's this. We have the Dirac Equation $$\left ( i \hbar \gamma ^{\mu } \partial_{\mu }-mc\right )\Psi =0$$ but for a local phase shift we have to let $$\Psi \rightarrow \Psi ^{'}= e^{i\alpha (x)}\Psi $$

If we do this we get an unwanted term, i.e. invarience is lost.

Therfore we put $$\partial\mu \rightarrow D\mu= \partial\mu - \frac{iq}{\hbar}A_{\mu}$$

From this we can define $$A_{\mu}^{'}=A_{\mu}+ \frac{\hbar}{q}\partial_{\mu}\alpha (x)$$

Which would then make the thing varient.

**My question**is how does this relate to the (b) question? is this what it is asking, I have no idea.

Any suggestions more than welcome!

for part (c) haven't I just done that? not sure what it wants.