Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I ##A_\mu^a=0## in global gauge symmetries ?

  1. May 17, 2018 at 11:34 PM #1
    Hi, this question is related to global and local SU(n) gauge theories.
    First of all, some notation: ##A## will be the gauge field of the theory (i.e: the 'vector potential' in the case of electromagnetic interactions) also known as 'connection form'.

    In components: ##A_\mu## can be expanded in terms of the basis given by the generators $F_a$ of a SU(n) group using some coefficients (or components) ##A_\mu^a## so one can write ##A_\mu=A_\mu^aF_a##.

    As you can see in the image I uploaded (from the book "An elementary primer for Gauge theory") one can identify ##A_\mu^a## wih the partial derivatives of the parameters ## \theta^a ## (in the last line you have ##A_\mu=\partial_\mu\theta^a\,F_a##) wich parametrize the infinitesimal ammount of transformation that is made by the operator ## U(dx) ## on an arbitrary vector u.

    The question is: If the transformation is global, i.e: ## \theta^a\neq f(x) ##, then... ## A_\mu^a=0 ## implies that is impossible to deffine a connection?.
     

    Attached Files:

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...