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vertices
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According to my notes "any pair of similar quarks must be in identical spin states". What is the reason for this?
In summary, according to the spin-statistics theorem, the "wavefunction" of a hadron in terms of quark and gluon degrees of freedom must be anti-symmetric under the exchange of two quarks. This means that any pair of similar quarks in a hadron must have identical spin states. This is due to color confinement and the requirement that all hadrons occurring in nature must be color singlets. In the case of mesons, which are bosons, the spin-space wavefunction of |quark,anti-quark> must be anti-symmetric in order for the overall wavefunction to be symmetric. However, in composite systems of quarks, the exchange symmetry may or may not be present.
- #2
humanino
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Hi
Very unclear. I do not expect the quark spin states in your left leg to be anyhow related to my grandmother's right arm quark spin states. So, which pairs are you talking about ?vertices said:
- #3
vertices
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for example |uu>, |ss>, |dd>... the spins must be pointing in the same direction.
even in hadrons, you can't have for example, the state |uus> having spins pointing |up-down-up> (the spins of u quarks have to be pointing in the same direction).
even in hadrons, you can't have for example, the state |uus> having spins pointing |up-down-up> (the spins of u quarks have to be pointing in the same direction).
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- #4
vertices
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can I ask another question:
due to colour confinement, the colour charge of a given state has to be 0 (a singlet). Therefore, the colour wavefunction is antisymettric.
Now mesons have to be symetric under exchange because they are bosons, right? So the spin-space wavefunction of |quark,anti-quark> has to be antisymetric too for the overall wavefunction to be symetric, right?
due to colour confinement, the colour charge of a given state has to be 0 (a singlet). Therefore, the colour wavefunction is antisymettric.
Now mesons have to be symetric under exchange because they are bosons, right? So the spin-space wavefunction of |quark,anti-quark> has to be antisymetric too for the overall wavefunction to be symetric, right?
- #5
humanino
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Quarks are fermions. Two identical quarks are undistinguishable inside a hadron. From the spin-statistics theorem, the "wavefunction" of a hadron in terms of quark and gluon degrees of freedom (assuming we can construct such a thing, although it should exist obviously in principle) must be anti-symmetric under the exchange of two quarks. It is one thing that is postulated, but for which people believe there should be a rigorous demonstration, that all hadrons occurring in Nature as free states must be color singlets. The color part of the wavefunction is therefore antisymmetric. So the rest of the wavefunction, in the space of flavor times spin times position for instance, should be symmetric. Note that the ground state, with the space part being obviously symmetric, has spin times flavor symmetric as well. So for two identical flavor, you get the symmetric spin state you were asking about.
- #6
vertices
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humanino said:
i see. It just gets a little bit confusing when you consider composite systems of quarks, because ofcourse quarks are fermions but a system of quarks in a given state, may not be - thus a composite state may or may not possesses exchange symettry.
many that humanin
1. What are quarks and what is their role in the spin states of particles?
Quarks are elementary particles that make up protons and neutrons, which in turn make up the nucleus of an atom. They have a property called spin, which is a measure of their angular momentum. In the context of spin states, quarks are responsible for determining the total spin of a particle.
2. What are the different spin states and how do they relate to quarks?
The two most common spin states are spin up and spin down, which refer to the direction of the particle's spin. In the case of quarks, they can either have a half-integer spin (such as 1/2 or 3/2) or an integer spin (such as 0 or 1). The total spin of a particle is determined by the combination of the spins of its constituent quarks.
3. Why are identical quarks in the same spin state?
This is due to a principle called the Pauli exclusion principle, which states that no two particles can occupy the same quantum state at the same time. Since quarks are identical particles, they must obey this principle. This means that if two quarks are in the same spin state, they must have opposite spins to avoid violating the exclusion principle.
4. Can quarks change spin states?
Yes, quarks can change spin states through interactions with other particles. This is known as spin-flipping and is a common occurrence in particle collisions. However, the total spin of the particle must remain conserved, so if one quark changes spin, another must also change to balance it out.
5. How do spin states of quarks affect the properties of particles?
The spin states of quarks play a crucial role in determining the properties of particles. For example, the spin of quarks contributes to the magnetic moment of particles, which affects how they interact with magnetic fields. The spin states also determine the stability and decay rates of particles, as well as their behavior in high-energy collisions.
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