Why do fermions have 1/2-integer spins?

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In summary, fermions have half-integer spins and obey the Fermi-Dirac statistics because of their antisymmetric wavefunctions. The connection between 1/2-integer spin and antisymmetric wavefunctions is explained by the spin-statistics theorem in QFT.
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lizzie96
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Hello,

Could anyone explain why fermions have half-integer spins and obey the fermi-dirac statics, whereas bosons have whole integer spins and don't? I have read lots of explanations at a fairly basic level for this, which say that this happens because fermions have antisymmetric wavefunctions. However, they do not fully explain the connection between 1/2-integer spin and antisymmetric wavefunctions. I've heard vaguely that there is an explanation for this in QFT (ie, spin and statistics are not just intrinsic properties that cannot be explained from other principles)... So could anyone explain or point me to a reference as to what the actual explanation IS?

Thanks!
 
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The result is known as the spin-statistics theorem. There's a proof on that wiki that is a bit short of details. There is a much more detailed proof explained in these notes that might be a better read, though in either case basic familiarity with QFT is assumed.
 

Related to Why do fermions have 1/2-integer spins?

1. Why do fermions have 1/2-integer spins?

The spin of a particle is a fundamental property that describes its intrinsic angular momentum. Fermions have 1/2-integer spins because they obey the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This means that fermions must have half-integer spin values (such as 1/2, 3/2, etc.) to avoid violating this principle.

2. What is the significance of fermions having 1/2-integer spins?

The fact that fermions have 1/2-integer spins has important implications in the behavior and interactions of matter. It allows for the formation of stable atoms, where electrons with opposite spins can occupy the same atomic orbital. This also leads to the diversity of elements and the complexity of the periodic table.

3. Can fermions have spins other than 1/2-integer?

No, fermions can only have spins that are half-integer multiples of 1/2 (e.g. 1/2, 3/2, 5/2, etc.). This is a consequence of the spin-statistics theorem, which states that particles with half-integer spin values must be fermions, while particles with integer spin values must be bosons.

4. How is the spin of a fermion determined?

The spin of a fermion is an intrinsic property that cannot be changed or measured directly. It is determined by the type of particle it is (e.g. electron, proton, neutron), and is a fundamental aspect of its identity.

5. Are there any exceptions to the rule of fermions having 1/2-integer spins?

Yes, there are a few exceptions to this rule. For example, in certain exotic systems such as quark-gluon plasmas, fermions can have non-integer spins. Additionally, in some theories beyond the standard model of particle physics, particles called anyons have fractional spin values. However, these exceptions are still subject to ongoing research and are not yet fully understood.

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