Dirac gamma matrices

  • Thread starter eoghan
  • Start date
  • #1
200
1
Hi!
I can define
[itex]\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3[/itex]
I know that the four gamma matrices [itex]\gamma^i\:\:,\;i=0...3[/itex] are invariant under a Lorentz transformation. So I can say that also [itex]\gamma ^5[/itex] is invariant, because it is a product of invariant matrices.
But this equality holds:
[tex]\gamma ^5=\frac{i}{4!}\epsilon_{\mu\nu\rho\sigma}\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}[/tex]
and this expression is not invariant!!
So, is [itex]\gamma^5[/itex] invariant or isn't it?
 

Answers and Replies

  • #2
fzero
Science Advisor
Homework Helper
Gold Member
3,119
289
[itex]\gamma^\mu[/itex] transforms like a 4-vector.
 
  • #3
200
1
But [itex]\gamma^5[/itex] transforms like a pseudo-scalar because of [itex]\epsilon_{\mu\nu\rho\sigma}[/itex]
 

Related Threads on Dirac gamma matrices

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
5K
Replies
3
Views
1K
Replies
0
Views
3K
  • Last Post
Replies
2
Views
894
  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
2K
Top