Gamma - traceless

  • #1
31
0
I read this question

https://physics.stackexchange.com/q...onditions-is-a-vector-spinor-gamma-trace-free . Also I read Sexl and Urbantke book about groups. But I dont understand why spinors is irreducible if these are gamma-tracelees. Also I read many papers about higher spin fields in which doesn't explain and proof gamma traceless(irreducibility condition) of spinors of higher rank. Can any explain this ?
 

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
12,994
548
Perhaps if we ping @samalkhaiat , you can get an answer. :) It may very well be the one on the SE website, though.
 
  • #4
31
0
Ok, it is clearer. But why 1/2 component carried with divergence of Dirac spinor ? (This removing ghosts ?)
 
  • #5
samalkhaiat
Science Advisor
Insights Author
1,710
971
Ok, it is clearer.
Is it? Then why are you asking this?
But why 1/2 component carried with divergence of Dirac spinor ?
First: [itex]\psi^{\mu}(x)[/itex] is a spinor-vector field. It describes spin-3/2 particle and its anti-particle. It is NOT a Dirac spinor (Dirac spinor field describes spin-1/2 particle and its anti-particle).
Second: The divergence of [itex]\psi^{\mu}(x)[/itex] IS a Dirac spinor because (as I have already explained in the other thread) [itex]\partial_{\mu}\psi^{\mu}[/itex] satisfies the Dirac equation. In other words, the field [itex]\psi (x) \equiv \partial_{\mu}\psi^{\mu}(x)[/itex] represents one of the two spin-1/2 components of the spinor-vector field [itex]\psi^{\mu}(x)[/itex]. All of this was explained in the other thread.
(This removing ghosts ?)
Which ghosts are these?
 
  • #7
samalkhaiat
Science Advisor
Insights Author
1,710
971
  • Like
Likes weirdoguy
  • #8
31
0
filip97
Can we raising and lowering indices of mwtric spinor with 2-contravariant or 2-covariant with metric tensor ? I think that we can do this with sigma(mu,nu) this write in Sexl Urbantke book of group representation. I was post this question because dont clear ho we contract Dirac equation with gamma(mu). Thanks a lot !!!
 

Related Threads on Gamma - traceless

Replies
8
Views
1K
  • Last Post
Replies
12
Views
6K
  • Last Post
Replies
10
Views
4K
  • Last Post
Replies
1
Views
808
Replies
3
Views
1K
Replies
9
Views
3K
Replies
2
Views
524
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
1
Views
4K
Top