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Homework Help: Peskin complex scalar field current

  1. Nov 4, 2017 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant 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^*##

    3. 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 ?
    Last edited: Nov 4, 2017
  2. jcsd
  3. Nov 9, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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