# Questions from Schwinger's particles, sources and fields

1. Nov 13, 2014

### MathematicalPhysicist

My first question from his first volume.

On page 254, he writes down the action expression:

$$(3-10.1)W=\int (dx)[K\phi+K^{\mu}\phi_{\mu}+\mathcal{L}]$$
Where the lagrangian is:
$$\mathcal{L}=-\phi^{\mu}\partial_{\mu} \phi +1/2 \phi^{\mu}\phi_{\mu} -1/2 m^2 \phi^2$$

The consideration of infinitesimal, variable phase transformations of the sources:

$$(3-10.2)\delta K(x) = ieq \delta \varphi (x) K(x) \ \ \delta K^{\mu}(x) = ieq \delta \varphi (x) K^{\mu}(x)$$

and of the compensating field transformations:
$$\delta \phi (x) = ieq \delta \varphi (x) \phi(x) \ \ \delta \phi ^{\mu} (x) = ieq \delta \varphi (x) \phi^{\mu}$$

gives directly (I don't see it how exactly, can someone show me?):
$$(3-10.4) \delta W = \int (dx) [\phi((x) ieq K(x) + ieq \phi^{\mu} K_{\mu} ] \delta \varphi (x)$$

I don't see how did he get (3-10.4), can someone elighten me.

Shouldn't he also take varaition of the lagrangian?!

2. Nov 18, 2014