Question

Can anyone briefly explain about quarks and yang-mills theory ??

Answer 1

Briefly? No, but here is an attempt to explain it none the less.

In the quantum theory of particle physics, quarks at the fundamental building blocks of matter, and hence are known as fundamental particles (this means that they have no internal structure, and cannot be broken down further). For example, 3 quarks are needed to make a proton or a neutron, and two a re required to make a meson. There are 6 types of quark, called up, down, strange, charm, top and bottom (or truth and beauty), and are defined by a property known as their quantum number. They also have fractional electric charges (1/3, and 2/3 the charge of the electron), as well as a property known as colour charge (not actually related to physical colour, but we needed a name for it). Whereas electric charge comes in two flavours (positive and negative), colour charge come in three flavours, red, green and blue (6 flavours if you include anti-red, anti-green and anti-blue). This colour interaction is mediated by force particles called Gluons, and they make up the strong nuclear force. Because of the colour notation, this branch of particle physics is called Quantum Chromodynamics (QCD), a play on Quantum Electrodynamics (QED), where colour takes on a role similar to electric charge.

This is all described under a mathematical framework known as a Yang-Mills gauge theory, which is a non-abelian guage theory. All very technical, but lets try to explain it a bit more. The term "non-abelian" just means that the equations do not commute. In mathematics this means that \(ab \neq ba\) or more plainly 3 x 2 is not teh same as 2 x 3, as the order of the operation is important. To clarify this, this is the same as baking a cake by a recipe that states to add water and bake for 20 minutes. The results would be different if you baked for 20 minutes, and then added water.

A gauge theory is a theory which obeys gauge symmetry (more strange terms, but bear with me). Gauge symmetry is a property of a field, where in the equations describing that field remain the same after one applies an operation to all particles everywhere in space. the term gauge just means "measure", and a field with gauge symmetry can thus be remeasured (or re-gauged) from different baselines without changing their properties. For example, if we had a ball on a step on a stair case, it would have a specific gravitational potential energy. If it then dropped down a step, it would loose a specific amount of gravitational energy due to the change of height with the earth's gravitational field. We can thus calculate the difference in energy between the two steps, but crucially, it doesn't matter where we measure the baseline to be (either from the lower step, higher step, top of the stairs, bottom of the stairs, centre of the earth, or geosynchronous orbit, or another galaxy entirely), the difference in energy will always come out the same, regardless of how you re-gauge the baseline.

Recall that a gauge theory, such as Yang-Mills theory, will obey gauge symmetry. We can imagine what gauge theory is by picturing a sheet of paper infinite in extent, all painted a specific shade of grey. Now no matter how you rotate the page, or whatever angle you look at it, it will appear just like any other angle. It is called globally invariant. This is true regardless of what shade of paint we use, re-gauging the colour makes no difference as per gauge symmetry. Now imagine though we take a similar sheet of paper, but painted in different shades of grey. The symmetry would then be broken, since we rotation or viewing angle, will change how it looks, since we will be able to distinguish different parts of the paper from others. We can restore the global invariance if we overlay the multi-shaded paper with a a clear plastic sheet that has been painted in shades that exactly balance the pattern in the paper (dark where the paper is light, and vice versa). The combined effect is to produce a uniform shade of grey with a global invariance.

What's this got to do with quarks etc? The multi-shaded paper represents the visible properties of a quantum field, and the sheet of plastic is the gauge field that which restores symmetry. Quantum fields will only present themselves when symmetry is broken. The basic ideas of QCD can be understood in terms of this symmetry and symmetry breaking. Please see the attached diagram. in this diagram a quark can have a "visible label" of red, green or blue, indicated by the uppermost letter on the diagram. We can transform the colour of the quark thorough a rotation of 120 degrees, so that it now has a new colour label. This is a symmetry operation. A symmetric global symmetry transformation would be to rotate every quark in the universe by 120 degrees, leaving the laws of physics unchanged. However, a single quark could under go a local symmetry transformation (and rotate 120 degrees), leaving the rest of the world unchanged. It is the need to restore this symmetry that we need to introduce new fields (Yang-Mills fields) which corresponds to the gluons of this gauge theory.

In physical terms, what this means is, any quark inside a hadron (that is a proton, neutron or meson) is free to change its colour independently of all other quarks in the universe, but that in order to satisfy gauge invariance, it must emit a gluon, which is absorbed by another quark, this gluon carrying a specific colour charge to satisfy the symmetry restoration. This exchange of colour charge is what binds quarks together to form protons and mesons. The exchange of colour charges is a bit more complex than this, but it gives a general. So Yang-Mills theory explains the mediation of the strong nuclear force in terms of a quantum field theory, in much the same way that Quantum Electrodynamics explains how the electromagnetic force works at the quantum level. In the latter, charged particles attract and repel each other through the exchange of photons, which are the mediators (or messenger particles) of the electromagnetic force.

Answer 2

thanx!! =))

Answer 3

and can you temme more about hadrons,mesons,bosons and fermions??

Answer 4

Hadrons are particles that are made up of quarks taht are bound together by the strong force. Protons and Neutrons are hadrons, but belong to a sub-group called baryons, hence why the machine in CERN is called the Large Hadron Collider, as it collides protons together (and it is quite large). Baryons will be made up of 3 quarks.

Mesons are a part of the hadron family, but are not part of the baryon family. Infact they belong to the meson family, meaning that they are made out of 2 quarks instead of 3.

The terms bosons and fermions are terms for different families of particles that exhibit specific properties. What distinguishes the difference between the two families is the nature of their quantum mechanical spin. For fermions the particles will have half integer spin (that is their spin will be \(\pm\frac{n}{2}\hbar\) where n is a \(n\) integer number. Fermions obey Fermi-Dirac statistics, and are subject to the Pauli Exclusion principle, and hence their properties define how the periodic table is formed.. Protons, neutrons electrons and quarks are all examples of fermions.

Bosons on teh other hand are particle with integer spin, meaning that their spins come in the form of \(\pm n\hbar\), again where \(n\) is an integer number. They obey Bose-Einstein statistics, but not the pauli exclusion principle. As a result they can all take on the same quantum state, which explains superconductivity, super fluidity, and bose-einstein condensates. Mesons, photons, and the hypothetical graviton are all bosons.

Note here that it is teh sum of the spins that determine if a partcicle is a fermion or boson. For example as mentioned before a proton consists of 3 quarks, each of spin \(\pm1/2\). You cannot add the spins of all three particles in any way to produce an answer that gives full integer of spin, hence the composite particle will have a half integer spin, and will be a fermion. Mesons on the other hand are made up of 2 quarks, and you cannot combine the spins in anyway to produce a total of half integer spin. Hence it will be a boson.

We can extend this to atoms. For example helium 3 (2 protons and 1 neutron) will be a fermion, but helium 4 (2 protons and 2 neutrons) will be a boson. this is why helium 4 exhibits superfluidity below a certain temperature, but helium 3 does not.

Answer 5

2 up quarks and 1 down quark make up a proton rite?! Then,what is neutron made up of?!

Answer 6

There are many types pf protons and electrons?!

Answer 7

1 up and 2 down make up a neutron. the charge of an up quark is 2/3, teh charge on a down quark is -1/3. Hence a proton has charge of 2(2/3) -1/3 = +1 and a neutron has a charge (2/3)+2(-1/3) = 0.

Answer 8

Only one type of proton that I know of, though there are 3 types of electron, known as the electron, muon, and tau (in order of increasing mass).