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Charge Conjugation Operation 
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#1
Feb510, 05:50 AM

P: 1,780

Hi,
According to Perkins (4th edition, pg 73 section 3.6) the operation of charge conjugation reverses the sign of the charge and the magnetic moment of a particle. Does this mean the spin also flips? But according to Griffiths, the spin is untouched by charge conjugation. What operation flips a particle to its antiparticle? I'm a bit confused, because I wrote in my class notes that spin flips under charge conjugation. But I don't see how it should. Thanks in advance. 


#2
Feb510, 06:19 AM

P: 527

A particle and it's antiparticle have the same spin, so it doesn't change under charge conjugation.
A particle's spin state is described by a state such as [itex]s,m\rangle[/itex]. The quantum number s is the spin, which is unaffected by charge conjugation, time reversal or parity. The quantum number m is the spin component along some axis and changes sign under time reversal alone. 


#3
Feb510, 06:45 AM

P: 1,780




#4
Feb510, 06:54 AM

P: 527

Charge Conjugation Operation
It flips the spin component [itex]n[/itex], not the total spin [itex]s[/itex] of the particle. A negative, total spin doesn't exist. It's the magnitude of the spin. A negative spincomponent does exist, and this indeed flips under time reversal.
Just for the record, the total spin is the eigenvalue of the spin operator squared, [itex]S^2[/itex]. The spin component is the eigenvalue of the spin operator along some particular axis, [itex] S_z[/itex] 


#5
Feb510, 07:07 AM

P: 1,780

Thanks for your reply xepma.
Also, what does the notation [itex]^{x}S_{y}[/itex] mean? I know it means a singlet spin state, but what do x and y denote? So many holes in my atomic physics :( [never did a course on atomic or nuclear physics. Did two courses on QM, never really encountered this notation.] I have another question, which I think is related: http://www.physicsforums.com/showthread.php?t=375609. EDIT: I think its just a matter of notation. Correct me if I'm wrong: you're saying [itex]S_{z}[/itex] flips sign under time reversal. The eigenvalue of [itex]S_z[/itex], denoted by [itex]m_s[/itex] therefore flips sign. The total spin angular momentum squared is [tex]S^2 = \boldsymbol{S}\cdot\boldsymbol{S}[/itex] and its eigenvalue is [itex]s(s+1)[/itex]. PS  Please have a look at the other question too. 


#6
Feb510, 07:30 AM

P: 527

Yea, by total spin I meant the [itex]s[/itex] in [itex]s(s+1)[/itex] which is the eigenvalue of the total spin angular momentum squared, [itex]S^2[/itex].
I agree with you that it can be a little confusing, because "spin" can really refer to the total spin, but also the spin component along some axis. These are, ofcourse, not really interchangeable. I haven't seen the notation [itex]^{x}S_{y}[/itex] before.. do you have a reference for it? We all have gaps in our knowledge. No shame in that :) 


#7
Feb510, 08:37 AM

P: 1,780

Also: http://www.physicsforums.com/showthread.php?t=375638 


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