# Charge Conjugation Operation

1. Feb 5, 2010

### maverick280857

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.

2. Feb 5, 2010

### xepma

A particle and it's anti-particle have the same spin, so it doesn't change under charge conjugation.

A particle's spin state is described by a state such as $|s,m\rangle$. 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. Feb 5, 2010

### maverick280857

That is not correct. Time reversal flips the spin (Table 3.2, Perkins, page 82). Parity does not. Perhaps you meant something else?

4. Feb 5, 2010

### xepma

It flips the spin component $n$, not the total spin $s$ of the particle. A negative, total spin doesn't exist. It's the magnitude of the spin. A negative spin-component does exist, and this indeed flips under time reversal.

Just for the record, the total spin is the eigenvalue of the spin operator squared, $S^2$. The spin component is the eigenvalue of the spin operator along some particular axis, $S_z$

5. Feb 5, 2010

### maverick280857

Ok I think I see why I'm so confused. When you said total spin $s$, did you mean $s^2$?

Also, what does the notation $^{x}S_{y}$ 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: https://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 $S_{z}$ flips sign under time reversal. The eigenvalue of $S_z$, denoted by $m_s$ therefore flips sign. The total spin angular momentum squared is [tex]S^2 = \boldsymbol{S}\cdot\boldsymbol{S}[/itex] and its eigenvalue is $s(s+1)$.

PS - Please have a look at the other question too.

Last edited: Feb 5, 2010
6. Feb 5, 2010

### xepma

Yea, by total spin I meant the $s$ in $s(s+1)$ which is the eigenvalue of the total spin angular momentum squared, $S^2$.

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 $^{x}S_{y}$ before.. do you have a reference for it?

We all have gaps in our knowledge. No shame in that :)

7. Feb 5, 2010

### maverick280857

I'm sorry I think this is called S-state (?). I came across something like this with a P instead of an S, in Perkins. Its supposed to be a favorite thing to put in PGRE

Particle Physics exam tomorrow morning