# what is the physical importance of unitary group

What would be the physical importance of unitary group? By physical, I mean geometric intuiton and the usages in physics.

Also, how would special unitary group be used?

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$\textrm{U}(1)$ is the gauge group of the electromagnetic force, $\textrm{SU}(2)$ is the universal cover of the rotation group $\textrm{SO}(3)$, $\textrm{SU}(3)$ is the gauge group of the strong force... – Zhen Lin Jul 8 '12 at 0:07

Also note that the gauge transformations from the gauge theories are local unitaries; you apply a different one in each spacetime point (which means that the actual group isn't one-parameter but infinitely-many parameters). That's why the $U(1)$ symmetry is relevant there: You definitely do $not$ get the same state if you do a local $U(1)$ transformation.