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Charge Conjugation Operation

  1. Feb 5, 2010 #1
    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. jcsd
  3. Feb 5, 2010 #2
    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 [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.
     
  4. Feb 5, 2010 #3
    That is not correct. Time reversal flips the spin (Table 3.2, Perkins, page 82). Parity does not. Perhaps you meant something else?
     
  5. Feb 5, 2010 #4
    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 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, [itex]S^2[/itex]. The spin component is the eigenvalue of the spin operator along some particular axis, [itex] S_z[/itex]
     
  6. Feb 5, 2010 #5
    Thanks for your reply xepma.

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

    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: 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 [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.
     
    Last edited: Feb 5, 2010
  7. Feb 5, 2010 #6
    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 :)
     
  8. Feb 5, 2010 #7
    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 :rolleyes:

    Particle Physics exam tomorrow morning :bugeye:

    Also: https://www.physicsforums.com/showthread.php?t=375638
     
    Last edited: Feb 5, 2010
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