Why do fermions have 1/2-integer spins?

[lizzie96]

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!

 

[jtbell]

This seems like it might be a good place to start, if you haven't seen it already:

http://en.wikipedia.org/wiki/Spin–statistics_theorem

 

[fzero]

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.