Solutions to first order equation with Clifford algebra elements

  • Thread starter gentsagree
  • Start date
  • #1
96
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.
 

Answers and Replies

  • #2
18,433
8,269
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?
 

Related Threads on Solutions to first order equation with Clifford algebra elements

  • Last Post
Replies
4
Views
2K
Replies
5
Views
1K
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
3
Views
1K
Replies
6
Views
534
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
Top