Charge conjugation for Dirac particles (error in problem?)

[nonequilibrium]

Homework Statement

Show that if $\psi$ is a down-spin anti-electron, and we apply charge conjugation, then $\psi^C$ is an up-spin electron.

The Attempt at a Solution

My calculations suggest that the anti-electron indeed becomes an electron; however, spin does not change for me. Is it possible that the above assignment is incorrect?

 

[andrien]

charge conjugation matrix is not diagonal in standard representation.so when applied to a negative energy electron spin down,it becomes spin up positive energy positron .

 

[nonequilibrium]

But then why does http://en.wikipedia.org/wiki/C_parity say that "Spin J" is not affected by charge conjugation?

 

[andrien]

j is total angular momentum quantum number.I am talking about intrinsic spin of the particle.In simple case,if we take spin simply as ( 0 1) ,it will become ( 1 0).

 

[nonequilibrium]

What's the diffrence between the total and intrinsic spin in this case? There is only the intrinsic spin here.

 

[andrien]

If you will notice ,it is the magnitude which does not change.the particle is spin 1/2 and it remains spin 1/2.

 

[nonequilibrium]

Do you have a source that claims that charge conjugation flips spin?

 

[andrien]

I am not saying that it flips spin.I am saying that since C matrix is not diagonal so when you apply it on a electron of negative energy spin down ,it makes the spin up of positive energy electron.but that is a different thing,the negative energy spin down electron describes a positron with spin up apart from some phase factor so when you apply charge conjugation on positron spin up ,you apply charge conjugation on negative energy electron spin down so it becomes positive energy electron spin up so both are having spin up.this seems correct by invoking hole theory.