## Three Families of Fermions

Posted by on Saturday, January 9, 2016 Under: Particle Physics

In my end of year review article a couple of weeks ago I made reference to the possible discovery of a Weyl fermion. Since then a few people have asked me what a Weyl fermion is and how it differs from a regular fermion. In fact there are three common types of fermions, and I thought I would give a brief review of them today.

Let me begin by explaining what fermions are. When quantum mechanics was being developed in the early 20th century, it was discovered that particles could exist in two possible forms. One option is the boson, which has the properties we observe on a classical level - it looks the same if you rotate it by 360 degrees (or sometimes by 180 degrees or 120 degrees or 90 degrees, or by any amount of rotation depending on its properties), and you can have any number of them present at the same time. (That explanation is perhaps too simplistic, but bosons are not the focus of this article.)

The other option that was discovered was the fermion, and it has very odd properties. Fermions have half-integer spins, which means they have different properties if rotated by 360 degrees, but will look the same if rotated by 720 degrees! It takes at least two complete rotations of a fermion to make it look the same as when you started. A short time later Pauli theorized and proved that fermions cannot exist together. If one fermion has a certain set of properties, then a second one will never have the same properties. (And that is a crucial fact, because it is what allows chemical reactions to occur, and therefore it allows the Universe as we know it to exist.). A third odd property of fermions is that they must be paired up with anti-particles that destroy fermions on contact. And perhaps the most important property is that every known form of matter is composed entirely of fermions. Everything is fermions!

The basic form of a fermion is called a Dirac fermion. This is the form that all matter particles take. These particles have a mass, and half-integer spin, and come in particle-antiparticle pairs. But soon after Dirac first published an equation that describes these particles, two other theorists found alternate forms for fermions.

The Majorana fermion has very similar properties to a Dirac fermion, but with one major difference. A Majorana fermion is a combination of a particle and antiparticle, and so it can annihilate with any other Majorana fermion of the same species. There is no difference between the particle and antiparticle. And one reason why these are very interesting to physicists right now is that the neutrino might be a Majorana fermion, although this is still very much debated and there is no definitive experimental evidence either way.

The third type of fermion was discovered by Hermann Weyl, and is thus known as a Weyl fermion. Mathematically it is possible to divide Dirac's equation, which describes the properties of fermions, into two separate equations with separate solutions. Each of these solutions describes a massless fermion, which is not possible with the other two types. It is also possible to recombine these two Weyl fermions into a single Dirac fermion, which has lead some to speculate on the possibility of fundamental Weyl fermions in nature.

Unfortunately no one has ever found any indication of a Weyl fermion in nature. But in July 2015 a team of scientists announced that they had created a low energy excitation of a crystal structure that behaved like a Weyl fermion. In a sense they mixed multiple fundamental Dirac fermions to create a composite particle that acts like a massless fermion.

While a fundamental Weyl fermion would be a much more interesting discovery, the fact that we can now make them in crystal structures in the lab will open up many new possibilities for studying these different types of fermions.

Let me begin by explaining what fermions are. When quantum mechanics was being developed in the early 20th century, it was discovered that particles could exist in two possible forms. One option is the boson, which has the properties we observe on a classical level - it looks the same if you rotate it by 360 degrees (or sometimes by 180 degrees or 120 degrees or 90 degrees, or by any amount of rotation depending on its properties), and you can have any number of them present at the same time. (That explanation is perhaps too simplistic, but bosons are not the focus of this article.)

The other option that was discovered was the fermion, and it has very odd properties. Fermions have half-integer spins, which means they have different properties if rotated by 360 degrees, but will look the same if rotated by 720 degrees! It takes at least two complete rotations of a fermion to make it look the same as when you started. A short time later Pauli theorized and proved that fermions cannot exist together. If one fermion has a certain set of properties, then a second one will never have the same properties. (And that is a crucial fact, because it is what allows chemical reactions to occur, and therefore it allows the Universe as we know it to exist.). A third odd property of fermions is that they must be paired up with anti-particles that destroy fermions on contact. And perhaps the most important property is that every known form of matter is composed entirely of fermions. Everything is fermions!

The basic form of a fermion is called a Dirac fermion. This is the form that all matter particles take. These particles have a mass, and half-integer spin, and come in particle-antiparticle pairs. But soon after Dirac first published an equation that describes these particles, two other theorists found alternate forms for fermions.

The Majorana fermion has very similar properties to a Dirac fermion, but with one major difference. A Majorana fermion is a combination of a particle and antiparticle, and so it can annihilate with any other Majorana fermion of the same species. There is no difference between the particle and antiparticle. And one reason why these are very interesting to physicists right now is that the neutrino might be a Majorana fermion, although this is still very much debated and there is no definitive experimental evidence either way.

The third type of fermion was discovered by Hermann Weyl, and is thus known as a Weyl fermion. Mathematically it is possible to divide Dirac's equation, which describes the properties of fermions, into two separate equations with separate solutions. Each of these solutions describes a massless fermion, which is not possible with the other two types. It is also possible to recombine these two Weyl fermions into a single Dirac fermion, which has lead some to speculate on the possibility of fundamental Weyl fermions in nature.

Unfortunately no one has ever found any indication of a Weyl fermion in nature. But in July 2015 a team of scientists announced that they had created a low energy excitation of a crystal structure that behaved like a Weyl fermion. In a sense they mixed multiple fundamental Dirac fermions to create a composite particle that acts like a massless fermion.

While a fundamental Weyl fermion would be a much more interesting discovery, the fact that we can now make them in crystal structures in the lab will open up many new possibilities for studying these different types of fermions.

In : Particle Physics