Does Charge Conjugation Flip Spin?

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  • #1
maverick280857
1,789
4
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.
 
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  • #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.
 
  • #3
xepma said:
The quantum number s is the spin, which is unaffected by charge conjugation, time reversal or parity.

That is not correct. Time reversal flips the spin (Table 3.2, Perkins, page 82). Parity does not. Perhaps you meant something else?
 
  • #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]
 
  • #5
Thanks for your reply xepma.

xepma said:
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]

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:
  • #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 :)
 
  • #7
xepma said:
I haven't seen the notation [itex]^{x}S_{y}[/itex] before.. do you have a reference for it?

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:

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

Particle Physics exam tomorrow morning :bugeye:

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

What is charge conjugation operation?

Charge conjugation operation is a mathematical operation that changes the sign of all the charges of a particle or a system of particles. It is used in the study of particle physics to understand the symmetries and properties of particles.

What is the purpose of charge conjugation operation?

The purpose of charge conjugation operation is to help physicists understand the symmetries and interactions of particles. It helps in the formulation of mathematical models that describe the behavior of particles and their interactions.

What is the difference between charge conjugation and parity operation?

Charge conjugation operation reverses the sign of all the charges of particles, while parity operation reverses the spatial coordinates of a particle. They are two different operations that together form the CPT symmetry in particle physics.

How does charge conjugation operation affect the properties of particles?

Charge conjugation operation does not change the mass, spin, or energy of particles. However, it can change the electric charge, weak isospin, and color charge of particles, which affects their interactions with other particles.

Can charge conjugation operation be observed in experiments?

No, charge conjugation operation itself cannot be observed in experiments. However, it plays an important role in the formulation of mathematical models that accurately describe the behavior of particles and their interactions, which can be tested and observed in experiments.

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