G-parity - where does the minus sign come from?

In summary, the conversation discusses the definition of G-parity as a combination of C-parity and a 180° rotation around the second axis of the isospin. The minus sign in front of the doublet when applying G-parity is due to not being in an eigenstate.
  • #1
Federica
12
1
Hi all,

I have a question on G-parity. I know it's defined as ## G = exp(-i\pi I_{y})C ##, with ##I_y## being the second component of the isospin and ##C## is the C-parity. In other words, the G-parity should be the C-parity followed by a 180° rotation around the second axis of the isospin.

Now, if I apply C on the isospin doublet ## \begin{pmatrix} u\\ d \end{pmatrix} ## I get ## \begin{pmatrix} \bar{u}\\ \bar{d} \end{pmatrix} ##, which is quite clear.

If I apply the G-parity on the same doublet I get: ## -\begin{pmatrix} \bar{d}\\ \bar{u} \end{pmatrix} ##. I understand ##\bar{d}## and ##\bar{u}## are now inverted because of the rotation around ##I_y##, but where does the minus sign come from?
 
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  • #2
Federica said:
but where does the minus sign come from?

The definition.

I am not sure what kind of answer would satisfy you. Why isn't "the definition" a good answer?
 
  • #3
Vanadium 50 said:
The definition.

I am not sure what kind of answer would satisfy you. Why isn't "the definition" a good answer?
I understand why the third component of the isospin changes its sign, that's because of the rotation. But why should I put a minus sign in front of the whole doublet?
 
  • #4
Sorry, I was confused about which minus sign you meant.

You are not in an eigenstate of G with the doublet you wrote. So -1 can't be the eigenvalue because there isn't an eigenvalue.
 

1. What is G-parity?

G-parity is a fundamental concept in particle physics that describes the symmetry of a system under the exchange of particles with their antiparticles.

2. Where does the minus sign come from in G-parity?

The minus sign in G-parity comes from the fact that antiparticles have opposite charge and parity compared to their corresponding particles. This results in a negative sign when exchanging a particle with its antiparticle.

3. Why is G-parity important in particle physics?

G-parity is important because it is a fundamental symmetry that helps us understand the behavior of particles and their interactions. It is also a key component in the Standard Model of particle physics.

4. How is G-parity related to other symmetries in particle physics?

G-parity is related to other symmetries such as charge conjugation (C) and parity (P). Together, these symmetries form the CP symmetry, which is conserved in strong and electromagnetic interactions but not in weak interactions.

5. Can G-parity be violated?

Yes, G-parity can be violated in certain rare processes involving weak interactions. This violation was first observed in the decay of the neutral kaon particle and has since been confirmed in other experiments. The violation of G-parity is important in understanding the origin of matter-antimatter asymmetry in the universe.

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