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Fermion

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Fermions are one of the two fundamental classes of subatomic particles. The other class is known as bosons. Every subatomic particle must belong to one of these two groups. Fermions are essential because they are usually associated with matter. They serve as the building blocks for the physical world around us.

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In particle physics, a fermion is defined as a particle that follows Fermi–Dirac statistics. This mathematical framework helps scientists predict how these particles behave in different environments.

One of the most important features of a fermion is its spin. Spin is a fundamental property of particles. Fermions always possess a half-integer spin, such as spin 1/2 or spin 3/2. This characteristic is linked to the spin-statistics theorem in relativistic quantum field theory. According to this theorem, particles with integer spin are bosons, while those with half-integer spin are fermions. Additionally, fermions possess conserved baryon or lepton quantum numbers. This means they carry specific, unchanging values that identify their type.

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Fermions must obey a strict rule called the Pauli exclusion principle. This principle states that only one fermion can occupy a particular quantum state at a given time. If multiple fermions share the same spatial probability distribution, they cannot be identical in every way. At least one other property, such as spin, must be different for each particle. This rule is why matter has structure and does not simply collapse.

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Without this principle, the atoms that make up our bodies would not function as they do.

Scientists categorize fermions into two main types: elementary and composite. Elementary fermions are not made of anything smaller. The Standard Model recognizes 24 different fermions in total. This includes six types of quarks: up, down, strange, charm, bottom, and top. It also includes six types of leptons: the electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino. Each of these also has a corresponding antiparticle.

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Composite fermions are made of multiple smaller particles. For example, a proton is a composite fermion because it contains three quarks. Because three is an odd number, the proton itself becomes a fermion.

Mathematics allows us to describe even more varieties of fermions. There are three common mathematical types: Weyl fermions, Dirac fermions, and Majorana fermions. Weyl fermions are massless particles. Dirac fermions possess mass and can be treated as a combination of two Weyl fermions. Majorana fermions are unique because each one is its own antiparticle. Most fermions in the Standard Model are believed to be Dirac fermions. However, scientists do not yet know if neutrinos are Dirac or Majorana fermions.

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In July 2015, researchers experimentally realized Weyl fermions in Weyl semimetals.

History shows us how these names came to be. The English theoretical physicist Paul Dirac coined the term "fermion." He named the particle class after the Italian physicist Enrico Fermi. This naming helps organize the complex world of quantum mechanics.

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The distinction between fermions and bosons is usually very clear. However, the current state of particle physics shows that this distinction can sometimes be unclear. Under extreme conditions, weakly interacting fermions can actually display bosonic behavior.

This strange behavior occurs when fermions form pairs. When they pair up, they can act like bosons. This process is responsible for superconductivity and superfluidity. In superconducting materials, electrons interact through the exchange of phonons to form Cooper pairs. In helium-3, atoms interact and pair through spin fluctuations to create superfluidity. There are also quasiparticles in the fractional quantum Hall effect called composite fermions. These consist of electrons with an even number of quantized vortices attached to them. This shows how even the most basic rules of matter can change in special environments.

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