Quarks transform under this representation of SU 3 , and because it's 3-dimensional we say quarks come in 3 colors: red, green and blue. This is just an amusing way of talking about the 3 column vectors. Alternatively, we could let elements of SU 3 act on row vectors by multiplication on the right. Antiquarks transform under that representation, and since it is also 3-dimensional we say they come in three colors as well: anti-red, anti-blue, and anti-green. This is just an amusing way of talking about the 3 row vectors.
Gluons transform under this representation, so there are 8 gluons. Or we could get. But, no matter how we take complex linear combinations of trace-zero hermitian matrices, we cannot get. So we cannot really get red anti-red. The closest we can get are things like. Objects are made of atoms, and atoms are likewise the sum of their parts—electrons, protons, and neutrons. Dive into one of those protons or neutrons, however, and things get weird.
Three particles called quarks ricochet back and forth at nearly the speed of light, snapped back by interconnected strings of particles called gluons. The problem is that, while the theory seems accurate, it is extraordinarily complicated mathematically. Faced with a task like calculating how three wispy quarks produce the hulking proton, QCD simply fails to produce a meaningful answer.
A million-dollar math prize awaits anyone who can solve the type of equation used in QCD to show how massive entities like protons form. Lacking such a solution, particle physicists have developed arduous workarounds that deliver approximate answers. But these approximation techniques have recently come into conflict, leaving physicists unsure exactly what their theory predicts and thus less able to interpret signs of new, unpredicted particles or effects.
To understand what makes quarks and gluons such mathematical scofflaws, consider how much mathematical machinery goes into describing even well-behaved particles.
A humble electron, for instance, can briefly emit and then absorb a photon. In the s, after considerable struggle, physicists developed mathematical rules that could accommodate this bizarre feature of nature. Studying an electron involved breaking down its virtual entourage into a series of possible events, each corresponding to a squiggly drawing known as a Feynman diagram and a matching equation.
A perfect analysis of the electron would require an infinite string of diagrams—and a calculation with infinitely many steps—but fortunately for the physicists, the more byzantine sketches of rarer events ended up being relatively inconsequential. Shmarks cannot be observed separately from atoms. If we consider them as "fundamental bricks", then their interaction is rather messy.
Add a comment. Active Oldest Votes. Mass gap implies confinement In order to understand why proving that the theory has a mass gap is equal to proving confinement, we first have to understand what confinement is.
Motivation The existence of confinement, while phenomenologically well-established, is not fully understood on a purely theoretical level. Improve this answer. I have a question about your sentence: "Since quarks and gluons themselves carry colour charge, this means that they cannot propagate freely, but occur only in bound states, so-called hadrons.
I thought it was generally believed that at very high energies quarks can occur as free particles, or have I misunderstood this? Yes, this is only true below the confinement scale. All the statements in my answer regarding confinement and mass gap are to be thought of in the context of low energy QCD.
As I mentioned in my answer, free gluons could have arbitrarily low energy, and as such contradict that the statement that there is a mass gap. Contrary to what you say, confinement does not imply a mass gap, as one can in principle construct confined states of zero energy e. Show 7 more comments. Ruma Dutta Ruma Dutta Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta.
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