B What does half-integer spin mean?

[Irfan Nafi]

I've read that this is one of the meaning that define a lepton and I was curious to see what this means. Other resources aren't being very clear.

 

[ChrisVer]

Half-integer spins define fermions (in which category leptons belong by having spin 1/2).
What is not clear?

 

[Irfan Nafi]

What half-integer spin means, as in what is it.

 

[ChrisVer]

What half-integer spin means, as in what is it.

Spin is a quantum number, and it takes half-integer or integer values. A fermion (half-integer spin particle) obeys the Pauli exclusion principle and so its total wavefunction has to be antisymmetric (it also obeys Fermi-Dirac statistics).
I can't give a more specific answer to a question that is supposed to cover a whole semester subject.

 

[fresh_42]

I've read that this is one of the meaning that define a lepton and I was curious to see what this means. Other resources aren't being very clear.

To answer this, it would indeed require some very theoretical background and mathematics. It's not easy to give such an answer on B level without using a technical language. This is likely the reason your sources haven't been very clear on this. @ChrisVer's answers already gave you a short glimpse.

You could think of it as one aspect on how we technically describe the properties of elementary particles by mathematical means or quantum theory at all.

Maybe the half-tones on a piano can be taken as an analogue (although a rather stretched one!). You only have the black and white keys - the whites as integer spins and the black ones as half-integer spins. And you have only a piano, no violins or so. So why are there black keys at all?

 

[triclon]

This does a good job explaining it: https://www.quora.com/What-is-spin-1-2

 

[nikkkom]

It has something to do that group of rotations in the usual 3d space has a "double cover group". It's a non-obvious concept, but rotation by 2x360 degrees "more fully" returns to the same state than rotation by only 360 degrees:



Because of this, on a microscopic level there are particles which are affected by rotation "only by half as much as usual" and they require a 720 degree rotation of the physical system to return to the same state. Those are particles with spin 1/2

 

[ChrisVer]

For the 720deg rotation thing, the normal vector on a Moebius surface can help illustrate that as an analogy (although it should only be seen as an analogy on a surface). But that is only true for spin-1/2, and not higher half-integer spins (3/2, 5/2 etc)

 

[gleem]

Uhlenbeck and Goudschmit introduced the concept of spin to explain the anomalous Zeemane effect suggesting the electron had a magnetic moment probably due to its spinning on an axis. The value of 1/2 was consistent with the degree of spitting of the electron orbitals of alkali metals in a magnetic field. Pauli had originally suggested the introduction of a quantum numbers of value ±½ to explain his exclusion principle with no physical interpretation. A physical interpretation was given as the rotation of the electron but Pauli rejected it because based on the estimated size of the electron at that time the surface would have to be moving faster than the speed of light. After the resolution of the anomalous Zeeman effect with the introduction of the electron magnetic moment Pauli accepted the interpretation..