How does spin relate to the symmetry of a particle?

[kregg87]

Why are particle with half integer spins anti-symmetric while integer spin particles are symmetric? Or in other words, how does spin relate to the symmetry of indentical particles?

 

[Nugatory]

This is the spin statistics theorem. Google will find many references (it's hard to overstate its importance) but I am not aware of any proofs that work for an I-level thread.

One thing you do want to be clear about (you may already know this, but it's not certain from your post): The symmetry and anti-symmetry we're referring to is a property of many-particle systems. If the wave function of the entire system changes sign when any two particles are exchanged, we say that is is anti-symmetric, while if the wave function is unchanged we say it is symmetric.

 

[vanhees71]

I'd say the proof in Weinberg's, Quantum theory of fields is the best one in the sense that it treats the general case of any spin. That's A level. In most other textbooks you find the treatment of the most simple cases of spin 0, 1/2, and 1 (relevant for the elementary particles in the Standard Model), which is I level. In Germany the introduction to QFT is in the advanced undergraduate course (leading towards an MSc degree).

 

[PeterDonis]

This article by John Baez might be helpful:

http://math.ucr.edu/home/baez/spin_stat.html