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When the gauge theory is quantized in the proper way, you cannot even meaningfully talk about the action of an $\mathrm{SU}(3)$ transformation on the space of states because the quantization of a gauge theory essentially requires you to quotient out the gauge transformations (all of them, including the global ones), so that they are "do nothing" ...

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Griffith's 1987 book correctly states a totally reasonable hypothesis, that the neutron's core is positive. Here's a simple model which probably goes back to Fermi: the neutron ought to spend part of its time as a virtual proton-$\pi^-$ pair, in a strong-interaction analog to the photon spending part of its time as an electron-positron pair; since the ...

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The nuclear force can be thought as the 'residual' of the strong force, just like the Van der Waals force is the residual of the electrostatic force. The carrier of the strong force are gluons and this is naively analogous to thinking of photons as being the carrier of the electromagnetic force. Quarks are fundamental particles, just like electrons. ...

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We don't know where quarks come from, anymore than we know where electrons come from. They are supplied by nature, as far as we know, as the basic elementary particles that the world around us is built upon. In the same way, we don't yet know why the speed of light is 300,000 m/s or what Dark Matter or Dark Energy are. We have a theory, called the Standard ...

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In fact, the Yukawa Lagrangian is (more or less) only the term $\mathcal{L}_Y = -g \bar{\psi}\psi \phi$. The (massless) Dirac Lagrangian for fermions and Klein-Gordon Lagrangian (plus potential) for the Higgs are not shown in your formula. The main difference between the Yukawa Lagrangian and the simpler $-g \bar{\psi}\psi \phi$ is that the Standard Model ...

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Because glueballs have energy, and $E = m c^2$ says that energy is equivalent to mass. (Or another way to say it is that if you "zoom out" far enough that you can't see the constituent gluons that form the glueball, than you just lump all their energy into an effective glueball mass.) The energy can be thought of as just being the kinetic energy of the ...

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If you had a gas of photons in a perfect cavity and these photons had energy $E~=~h\nu$, then for $N$ photons the cavity would have a mass $m~=~Nh\nu/c^2$ of photons. Glueballs as similar. The gluon carries two color charges (really color plus anti-color) and they can interact with each other. This forms a self-bound system that confines the massless gauge ...

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Because in relativity the mass of a collection of particles is not necessarily the sum of the masses. Even two photons (treated as a unit) can have mass. Consider the total four-vector of a system with component four-vectors $(E,\hat{z}E/c)$ and $(E,-\hat{z}E/c)$. It has mass $(mc^2)^2 = (2E)^2$.

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As the comments say, one has to use Feynman diagrams in order to easily understand quantum number conservation and energy momentum conservation. Let us take the simple case of a high energy photon creating an e+e- pair. Here is the Feynman diagram of an incoming gamma ray creating an e+e- pair: which conserves energy, momentum and lepton quantum numbers. ...

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Yes, pair production is possible for quarks in the same way that for electrons or muons. But there are two caveats: QCD has a nasty property called confinement: quarks themselves can't exist isolated in nature, they must be inside a meson or baryon. In fact, they usually produce jets of such particles. Electrons are much lighter than quarks, and of course, ...

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Part 1: The branch of string theory which actually tries to match experiment is called string phenomenology. The state of the art in string phenomenology is that, starting from different forms of string theory (heterotic string theory, M-theory, F-theory...), it is possible to define space-time geometries, arrangements of branes, background fluxes... such ...

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I will address the title question: does string theory explain the existence of 3 generations of quarks leptons because of the word "explain". Physics is about measurements and observations and mathematical models which not only fit the measurements and observations but also have predictive power. Otherwise the model is just a map, not a physics theory....

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The official string theory website says this: Theoretical physics has not explained why there are three generations of particles that make up matter. Maybe string theory will come up with an answer for this. That's really where it stands. In fact, there's another question on physics SE here, where one of the answers says The question as to why ...

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