That's true, so what's the point of introducing SU(3) flavor/isospin symmetry?
Is it true that the strong Hamiltonian is to a good approximation just a function of the SU(3) flavor Casmir, H=H(\Sigma_{i=1}^{8} T_{i}^2) ? Or can one only say it is to a good approximation just a function of the...
Can you symmetrize the uud if you wanted to? Can it be:
|\Delta^+ \rangle =(|uud \rangle+|udu \rangle+|duu \rangle)\otimes |\uparrow \uparrow \uparrow \rangle instead?
This wavefunction has the nice property that it transforms in the SU(3) decuplet. With just uud, then it no longer transforms...
I still don't understand antisymmetry and fermions.
Is the proton wavefunction equal to this:
|\psi_p>=\frac{1}{\sqrt{6}}\left(2|u\uparrow u\uparrow d \downarrow \rangle -
|u\uparrow u\downarrow d \uparrow \rangle -
|u\downarrow u\uparrow d \uparrow \rangle \right)
or this...
I tried the calculation again, this time with:
(ud+du)(\uparrow \downarrow+\downarrow \uparrow)
or the direct product of two symmetric states instead of two antisymmetric states, then I symmetrized it all with a u-up quark. It can be easily seen that you get the d quark with spin down by...
I have no idea. Just to give you an idea of things you can do in this SU(6) model, consider this wavefunction, where arrows refer to spin.
(ud-du)(\uparrow \downarrow-\downarrow \uparrow)
In order to get a spin up proton, you need to add a u-quark with an uparrow.
Now normally if you...
Well just to show you that I'm not completely crazy, here's Wikipedia:
http://en.wikipedia.org/wiki/Quark_model#Baryons
"approximate symmetry is called spin-flavour symmetry".
The 56 comes from the symmetric state in SU(6): 6*7*8/3!
For some reason they're taking the direct product of spin...
If you just consider u,d,s, then SU(6) with the 6 components u +-, d+-, s+-; where + and - refer to spin up or spin down; gives the correct wavefunctions including spin.
If you just consider SU(3) with u,d,s, then this doesn't take into account spin, and you get weird things such as separate...
Re: isospin
Thanks.
I was under the impression that the Pauli exclusion principle and antisymmetry only applies to indistinct particles. If one of the particles is slightly different than the other - however slight the difference - then they are distinct particles. So I don't think...
Why is a deuteron an antisymmetric singlet in isospin:
|\uparrow\downarrow>-|\downarrow\uparrow>=|0,0>
whereas a proton and neutron that are separated are a combination of an antisymmetric singlet and a symmetric triplet:
|\uparrow\downarrow>=|0,0>+|1,0>
I don't understand the difference...
Why is it that the group SU(6) gives you the correct wave function for hadrons made up of the u, d, and s quarks? The 6 elements in the fundamental representation would be u up, u down; d up, d down; s up, s down. What's the meaning behind SU(6)?
Also, for 6 quarks, would it be SU(12)?
Why are spin 0 mesons pseudo-scalar, and spin 1 mesons vector?
Why can't spin 0 mesons be scalar, and spin 1 mesons be pseudo-vector?
If observables are bilinear in the fields, then how can you even detect whether a field is pseudo-scalar, since \phi^2 is a scalar no matter if the meson field...
How did you derive this? The state is certainly symmetric, but how does one know that this doesn't come from the direct product of symmetric flavor states and symmetric spin states?
For a mixed state I only know this formula:
\psi=\psi_{ijk}+\psi_{jik}-\psi_{kji} -\psi_{jki}
If I can't use...
Why is the product of a mixed symmetry state (spin) with another mixed symmetry state (flavor) altogether symmetric?
Say you symmetrize i and j, and then antisymmetrize i and k:
\psi=\psi_{ijk}+\psi_{jik}-\psi_{kji} -\psi_{jki}
So let ijk=uud, then:
\psi=2uud-duu-udu
Now swap...
That helped a lot. It bothered me because everyone says its hundreds or it's a zoo, and I just couldn't understand why people couldn't just say how many there are, since naively 6*6*6=... But I forgot about orbital angular momentum, so I guess you can go beyond 3/2 for baryons and 1 for mesons...
I keep on hearing that there are hundreds of hadrons, or even more ambiguous a zoo of hadrons, but for some reason I've never seen an exact answer.
Given that there are 6 quarks, it seems you can form 6*6*6=216 baryons. Including anti-baryons, that would be 2*216=432 baryons. Also there are...
When does the Yukawa potential apply and when does the scattering matrix apply?
Take QED for example. When calculating a scattering amplitude, you have an expansion in powers of the fine structure constant, 1/137. Where does Coulomb's law F=e^2/r^2 come in? As far as I can tell, all...
For two sources of the same charge, the exchange of spin zero particles produces an attractive force, the exchange of spin one particles produces a repulsive force, and the exchange of spin two particles results in an attractive force. Mass doesn't matter, just spin. The pattern is +-+-+- (where...
I'm a little confused now about what hadronization really is.
I thought that if the temperature is around 1 GeV, then quarks and gluons exist freely.
The LHC is colliding protons at the TeV scale, so the quarks and gluons are still hadronized into a proton at 1 TeV.
So what's going on...
Actually, I just remembered that I once went through the calculation to prove confinement.
Here's how I remember it:
When the coupling is really large, you can define the action in terms of Wilson plaquettes. What this does is turn the coupling from g^2 to 1/g^2, so now the coupling is really...
lol, I agree it's just semantics. When you measure a parameter, it's physical in the sense that you just measured a real cross-section to get that parameter. So it's a physical result.
I was probably sloppy with terminology.
I do recall that to motivate the definition of the path integral, a discrete path is considered first. This is done by putting discrete number of completeness relations between the initial position state and the final position state, and each completeness relation corresponds to a sum at that...
I never thought about it like that. But yeah 32x32x32x32 is 10^6, and 32 points is nowhere close to infinity. And of course scalar theory with just one kind of scalar is easiest. So I won't even attempt to try a calculation with a computer. But I am still interested in how its's done in...
I don't think we can measure \Lambda_{QCD}. For example, on page 6 of a layperson's introduction to QCD:
http://www.frankwilczek.com/Wilczek_Easy_Pieces/298_QCD_Made_Simple.pdf
there is a nice figure of QCD experiments and their measured value for the strong coupling. At the lowest energies...
I just looked at the Wikipedia page for the RHIC and it says temperatures of 7 trillion Kelvin were reached. Multiplying by Boltzmann's constant I get half a GeV.
This seems to be a little too close to \Lambda_{QCD}=.2 \mbox{ }GeV.
Does hadronization occur exactly below .2 GeV, so that if...
So take a 2x2 scattering with 4-momenta: a, b, c, and d (the difference between incoming and outgoing particles I guess would be determined by whether the energies are positive or negative). So J(k)=\delta^4(a-k)+\delta^4(b-k)+\delta^4(c-k)+\delta^4(d-k) and:
W[J(k)]=\int...
What is the basic idea behind lattice theory or computer-based QFT calculations?
For example, take a scalar field, and the functional path integral:
W[J(x)]=\int [d\phi(x)]e^{i\int \mathcal L \mbox{ }d^4x+i\int J(x)\phi(x)d^4x}
W[J] is the starting point for all types of...
Thanks! That was very helpful.
My main area is more towards neutrinos, but I feel to be well-rounded at physics, I need to know some things about QCD so I can follow what's going on in the accelerators because that's the big news in physics, the restart of the LHC.
I'm learning in statistical mechanics that temperature is a phenomenon that requires lots of particles at equilibrium to define (or something like that: I was a bit unclear what the teacher was talking about): T=\frac{\partial E}{\partial S} at constant particle number and volume .
I've also...
When you say "some other particle yet to be discovered", would this particle have to be greater than 200 GeV in mass, since LEP reached those energies? I know you're talking about a virtual particle, but even if it's 300 GeV in mass, you will see signs of it through the effects on the...
In e+e- annihilation, are the jets that are produced quarks and gluons, or hadrons?
What is the basic idea behind a QCD calculation for such a process? For example, do I take the two initial states to be e+e-, and the two final states to be q+q- (quark and antiquark), but also add the...