Forty years ago, in 1969, was awarded the Nobel Prize in physics Murray Gell-Mann, for his discoveries about elementary particles. If there is anything that stands in the line of discoveries and ideas of Gell-Mann is the beauty and harmony. The eightfold path eightfold way or in English, is the tip of the iceberg of the wonderful world of symmetries in particle physics.
Symmetries and conserved charges
The universe is full of symmetries that are observed by some systems. That is, there are actions which, taken on some systems, they leave their physical properties invariant. Example. Imagine a capacitor with two infinite conducting plates and parallel to each other and both perpendicular to z axis, located at z = - L, z = + L. Between them there is an electric field parallel to z axis This system has a clear translational symmetry in two directions: the two directions x, y parallel to the plates. The situation is identical in regardless of where point x, and we place ourselves. If one imagines these two infinite plates, the system has translational symmetry in the two directions perpendicular to the z axis One of the most important physics of the last century is Noether's theorem. This tells us more or less that there is always such a burden symmetries preserved. The term load must be understood in a general context, and not just think in the electric charge for instance. In the above example, Noether's theorem tells us that two charges will be preserved one for each symmetry: one along the x axis, another along the y-axis These conserved quantities are found to be the components x, and momentum px, py.
suppose to understand between the plates put an electron. There are no forces in the plane x, y, and thus according to Newton's second law of linear momentum px, py of the electron is conserved. The shape of their movement is independent of the point in the plane x, and which is initially. Momentum is different in z (pz). Since there is an electric field in z, pz happen that will change over time according to Newton's second law. In contrast px, py are always kept constant while the electron moves between plates.
What values \u200b\u200bcan take these charges conserved? Each px, py infinite value on the real line. Whatever, this value is always constant. In short, nothing changes in the electron and its state of motion by moving it in x, y. This fact results in the conservation of momenta px, py.
Isospin and symmetry between neutron and proton
One of the bright ideas of Werner Heisenberg was to propose that there is a symmetry between proton and neutron, so that nothing changes in exchange for one another. At first glance this may seem surprising, since both have electric charges and different masses, but works with simplified physics. The mass between the two is very similar, so that Heisenberg seemed reasonable to think at first that in a universe without electromagnetic interaction the proton and the neutron would be absolutely identical - even the mass difference could be due to the electromagnetic interaction, thought.
This symmetry postulated by Heisenberg's really an expression of symmetry between the quarks that make up the proton and the neutron. These are the up and down (u, d). Its mass is very similar, but differ in electrical charge. What is this kind of symmetry between u, d? In the previous example we saw a symmetry travel in space, here is a symmetry of rotation in an internal space. In this approach or should appear simplifación therefore a conserved charge, which is known to isospin.
What values \u200b\u200bwill take charge of isospin conserved? Well, the answer to this question is one of the finest episodes of quantum theory - and whose justification is beyond the scope of this post. Mathematics show that, contrary to translational symmetry to rotational symmetries are possible discrete values. To specify a state of isospin requires two numbers. The situation is similar to the case spin. Such an electron has spin 1 / 2 and the projection of this spin on a particular axis will be +1 / 2 or -1 / 2 depending on the orientation of the electron from the axis. In the case of isospin has to be equal and both u and d are isospin 1 / 2 and the projection of this are u = +1 / 2, d = -1 / 2. As with the projection of spin, for the projection of isospin values \u200b\u200bis worth taking-I,-I +1, ... I-1, I, in steps of 1 from minus the value of isospin to the value of isospin (ie -1 / 2, +1 / 2 for isospin of 1 / 2, -1, 0, 1 for an isospin of 1).
Projection spin for a spin 1 / 2, details of the spin and the theory of rotations for example in the Wikipedia
turn the spin of the quarks is 1 / 2, both of u and the d. Unlike the spin isospin not allow us to classify in groups of two particles - that is, or in one of +1 / 2 and a -1 / 2 depending on the projection on an axis, since this projection depends on our choice of the coordinate axes - and physics is independent of them. That is, the projection of spin mixing in a single particle and is not associated with types of particles. Isospin projection, by contrast, is in an internal space symmetry where such freedom does not exist in principle.
In short, we have two quarks with two different values \u200b\u200bof the projection of isospin, and with the same spin. On the other hand, have different electrical charge. However, we have said that the electromagnetic interaction we will ignore.
Now we construct baryons, which are combinations of three quarks, with the same spin. That electric charge is equal to or not in these combinations we traro not care. Let us first consider combinations of u, d. What combinations are possible? As we have uuu, ddd, udd, uud. Of these combinations, in its ground state combinations uuu, ddd have spin 3 / 2, while that combinations udd, uud spin 1 / 2. uud and udd combinations of spin 1 / 2 correspond to the proton and neutron respectively. In these combinations as two quarks are always u and d, the value of the isospin projection of the third quark is inherited. So have isospin 1 / 2 and the projection 1 / 2 and -1 / 2 respectively.
The octet of baryons
addition to considering the quarks u, d we can also consider the s quark (strange = weird). Its mass is not as similar as those of u, d, but we can also apply to some simplification would be a symmetry between the states formed by three quarks. As we have classified the states of isospin +1 / 2 and -1 / 2 to obtain a group of two particles with very similar mass, we can classify the states of isospin + surprised (by convention strangeness -1 if the combination has a strange quark , -2 if you have two, etc..) and get a group of particles with similar masses.
As mentioned before, we distinguish between those combinations of spin 1 / 2 and those of spin 3 / 2. The same combinations of three quarks can only have spin 3 / 2. We focus on combinations of spin 1 / 2. These are as follows.
With zero s quarks: uud, udd
With
an s quark: uus, uds, dds
With two s quarks: uss, dss
- What values \u200b\u200bof the projection of isospin will these combinations? In the background is clear. For example, will uss uss = +1 / 2 and dss = -1 / 2, both inherited from the value of the isospin projection of u, d, respectively. The following table shows the combinations of spin 1 / 2 with its values \u200b\u200bof isospin and strangeness, and isospin projections possible and the names of these baryons:
- Now what we do now is draw these combinations a plane with horizontal axis with the projection of isospin I3 and shaft strangeness S. vertical Get this (in this diagram are drawn also the electric charge Q and hypercharge Y):
Anyone who sees this classification for the first time this diagram can not help but wonder about the fascination of particle physics. The beauty of this classification led to its inventor, Murray Gell-Mann, to call it eightfold way, eightfold path, referring to
noble eightfold path of Buddhism. The eightfold path of Gell-Mann is the beginning of the adventure of particle physics, a story of discovery each more beautiful and profound. Other combinations
Ratings
are similar to the case of baryons with spin 3 / 2, in which case it is not a byte but a group of ten items, also for mesons (composed of a quark-antiquark pair). ratings have also been adding additional quarks and quantum numbers. That is, besides u, d, s, also consider the quarks c, b, t. Adding for example the quark c (charmed, charm) must be added a further dimension to the diagram is something like (the subíncie represents the number of c quarks in combination) - where our octet is in the database:
Differences mass start making these symmetries unsustainable and unhelpful, and also ratings over u, d, s, c, are no longer viewable.
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