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Spinor Problems

  1. Jan 15, 2013 #1
    I'm working through some spinor calculations in the following book:
    http://books.google.co.uk/books?id=...ame as complex conjugate for a scalar&f=false

    On p54 and p55, I have a few things that are troubling me:

    (i) Underneath (3.75), he notes that for D=2,3,4,10,11, we have -t_0t_1=+1 (see Table 3.1 for t_r values) and so the Majorana conjugate of the charge conjugate will be equal to the Dirac adjoint of the spinor. What is the significance of this statement?

    (ii) How do we derive (3.77)-(3.79)? I cannot make much headway.

    For example, my attempt to prove (3.77) is as follows:
    [tex] (\gamma^\mu)^C = B^{-1} (\gamma^\mu)^C B [/tex]
    [tex] = i t_0 \gamma^0 C^{-1} (\gamma^\mu)^* i t_0 C \gamma^0 [/tex]
    [tex] =i^2 t_0^2 \gamma^0 C^{-1} (\gamma^\mu)^* C \gamma^0 [/tex]
    [tex] =-\gamma^0 C^{-1} (\gamma^\mu)^* C \gamma^0 [/tex]
    where we've used [tex]B=it_0 C \gamma^0 \Rightarrow B^{-1}=-i t_0 (\gamma^0)^{-1} C^{-1} = i t_0 \gamma^0 C^{-1}[/tex]

    Now the problem is that we have something involve the complex conjugate of the gamma matrix. If we had something involving the charge conjugate then we could substitute from (3.45) and be finished. I cannot see how to get from here to what they have in (3.77)

    Thanks.
     
  2. jcsd
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