🚀 go-pugleaf

<CCB104@psuvm.psu.edu> writes:
>I heard it said by a former physics grad student that a certain professor
>of his said that it is *obvious* why there is "no spin in 2 dimensions"
>(i.e. in a 2-dimensional differentiable manifold of some sort?). What might
>they have meant, please? Any ideas?

Just taking a guess at what the professor might have meant:

In QM, the commutator of any two different angular momentum operators is
a constant times a third angular momentum operator linearly independent
of the other two.  If you have two dimensions and only two independent
angular momentum operators, what is their commutator?  Since you can't
produce something with the algebra of an angular momentum in 2 dimensions,
any set of "spin" operators you do produce can't properly be called an
angular momentum.

Classically, which direction does the cross product, RxV, point in two
dimensions?  (Though you can get around this by saying that angular
momentum isn't the pseudo-vector RxV but rather a rank 2 antisymmetric
tensor).

     Richard M. Mathews			F oster 
					 E stonian-Latvian-Lithuanian
Richard.Mathews@West.Sun.COM		  I ndependence and
					   F reedom!