1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Use of the conservation equation for Noether currents

  1. Jun 23, 2015 #1
    1. The problem statement, all variables and given/known data

    Given that

    ##\frac{dQ'}{dv} = \frac{1}{c^{2}} \int d^{3}x \bigg[ x \big( \frac{\partial \rho}{\partial t} - \frac{v}{c^{2}} \frac{\partial j^{x}}{\partial t} \big) - j^{x} \bigg] \bigg|_{t = \frac{vx}{c^{2}}, x, y,z}##,

    use the conservation equation ##\partial_{\alpha} j^{\alpha} = 0## to show that the integrand is a total derivative.

    2. Relevant equations

    ##\bigg( \frac{\partial}{\partial x} j^{x} \big( \frac{vx}{c^{2}},x,y,z \big) \bigg)_{y,z} = \bigg[ \frac{v}{c^{2}} \frac{\partial j^{x}}{\partial t} + \frac{\partial j^{x}}{\partial x} \bigg] \bigg|_{t = \frac{vx}{c^{2}}, x, y,z}##

    3. The attempt at a solution

    I understand that there must be a total derivative before the integrand. I understand that ##\frac{d}{dt}## is one example of a total derivative. But, how is the concept of total derivative generalised in an arbitrary number of dimensions?
     
  2. jcsd
  3. Jun 28, 2015 #2
    Thanks for the post! 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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Use of the conservation equation for Noether currents
  1. Noether Currents (Replies: 13)

  2. Noether Current (Replies: 1)

Loading...