🚀 go-pugleaf

Richard.Mathews@West.Sun.COM (Richard M. Mathews) writes:
   <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"

   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?  

In fact, in two dimensions there is only _one_ angular momentum operator --
along the axis normal to the plane. There's nothing for it not to commute 
with, at all.

   Classically, which direction does the cross product, RxV, point in two
   dimensions?  

It doesn't point at all: only one of the three components of (the 3-D) RxV
is ever nonzero (in 2-D), so it's best to think of it as a scalar...
(though in 2-D relativity it probably isn't _really_ a scalar quantity;
but then QM doesn't work too well with SR anyway...)
--
Craig DeForest -- astrophysicist for hire.   DoD#314159; PhD#271828