there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = -1/2. These correspond to quantum states in which the spin component is pointing in the +z or −z directions respectively, and are often referred to as "spin up" and "spin down"

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Leptons as fermions
Spin-1/2 particles so far
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there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = -1/2. These correspond to quantum states in which the spin component is pointing in the +z or −z directions respectively, and are often referred to as "spin up" and "spin down".
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Leptons are spin 1/2 particles. The spin-statistics theorem thus implies that they are fermions and thus that they are subject to the Pauli exclusion principle: No two leptons of the same species can be in the same state at the same time.
Furthermore, it means that a lepton can have only two possible spin states, namely up or down.
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sz is the spin projection quantum number along the z-axis.
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics and generally has half odd integer spin 1/2, 3/2 etc. These particles obey the Pauli exclusion principle.
Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei.
Fermions differ from bosons, which obey Bose–Einstein statistics.
Some fermions are elementary particles, such as the electrons, and some are composite particles, such as the protons.
According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
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