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## Main Question or Discussion Point

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

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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

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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/ [Broken]

http://mathworld.wolfram.com/LieGroup.html

http://en.wikipedia.org/wiki/Lie_group

http://physics.harvard.edu/~dtlarson/tutorial05/ [Broken]

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HallsofIvy

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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!

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U(1) corresponds to photon

SU(2) to W's and Z's

SU(3) to the gluons.

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