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

Solutions to first order equation with Clifford algebra elements

  1. Nov 18, 2014 #1
    In the same way one can show that [itex]\nabla^{2}\theta=0[/itex] has only one smooth solution, namely [itex]\theta=0[/itex], I would like to show that

    [tex]\gamma^{i}\partial_{i}\epsilon=0[/tex] has only one smooth solution, where [itex]\gamma^{i}[/itex] is a Dirac gamma matrix (or an element of the Clifford algebra), and [itex]\epsilon[/itex] is a spinorial quantity (which may or may not be relevant to finding a smooth solution, I am not sure).

    Any advice?

    Also can anyone recommend a book that treats formally (and clearly, possibly) a procedure for finding unique/smooth solutions to equations.

    Thanks.
     
  2. jcsd
  3. Nov 23, 2014 #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