Peskin complex scalar field current

[Dansuer]

Homework Statement

i'm trying to calculate the charge operator for a complex scalar field. I've got the overal problem right but I'm confused about this:
On page 18 of Peskin, it is written that the conserved current of a complex scalar field, associated with the transformation $\phi \rightarrow \phi e^{\alpha \phi}$, is
$$ j^\mu = i(\partial^\mu \phi^*) \phi - i \phi^* (\partial^\mu \phi)$$
I'm trying to recalculate it.

Homework Equations

$$ j^\mu = \frac{\delta L}{\delta (\partial_\mu \phi)} \delta \phi +
\frac{\delta L}{\delta (\partial_\mu \phi^*)} \delta \phi^* $$
$\delta \phi = i \phi$ and $\delta \phi^* = -i \phi^*$

The Attempt at a Solution

Using the above equations i get
$$ j^\mu = i(\partial^\mu \phi^*) \phi - i (\partial^\mu \phi) \phi^*$$
and since i will later promote $\phi$ to an operator the order is important. Or not ?

 

[member 553083]

Because when i calculate the charge operator, which is the time component of the conserved current, I get a different answer than the one in Peskin.Where am i wrong ?