SU(3), U(1), O(3), etc what are they?

[cefarix]

I've heard them used before...some sort of symmetry, but I never figured out what it really is. Can someone please explain the concepts to me? thx

 

[robphy]

Those are examples of "Lie Groups".
http://mathworld.wolfram.com/LieGroup.html
http://en.wikipedia.org/wiki/Lie_group
http://physics.harvard.edu/~dtlarson/tutorial05/

 

[HallsofIvy]

SU(3) is the "special unitary group of order 3": 3 by 3 complex matrices with determinant 1

O(3) is the "orthogonal group of order 3": 3 by 3 real matrices with determinant 1 or -1

U(1) is a bit puzzling! I would interpret U(n) as the "unitary group of order 3": n by n complex matrices with determinant 1 or -1. But "1 by 1 matrices" are just numbers. I guess U(1) would be the multiplicative group with members 1, -1, i, and -i!

 

[robousy]

You will here them used to describe different types of standard model features.

U(1) corresponds to photon
SU(2) to W's and Z's
SU(3) to the gluons.