U(1):?:SU(3) 1D:2D:3D harmonic oscillator.

[Spinnor]

The one dimensional harmonic oscillator is associated with the group U(1) and the three dimensional harmonic oscillator is associated with the group SU(3). Is their a group associated with the two dimensional harmonic oscillator?

Thank you for any thoughts.

 

[Spinnor]

I was given the hint by Igor, thoovler@excite.com:

"What simply connected special unitary group is bigger
than U(1), but smaller than SU(3)?"

My guess was SU(2), a Google search seems to confirm this.

 

[Ben Niehoff]

Yes, I think you are correct. If you have a copy of Goldstein (Classical Mechanics), they discuss this, as well as the SO(4) symmetry of the 1/r potential.