The physical meaning of a symmetry

[Planck const]

I know that the physical meaning of SU3 and SU2 - you can change the places of the quarks or/and leptons and you will get the same results.

What is the physical meaning of U1, and O3,1 (Lorentz group if I am not wrong)?

I know U1 is connect with the Polarization of the light.

Thanks very much to the people who will answer... (sorry about my bad english)

 

[Naty1]

It seems many of the laws of physics originate in symmetries.

You might find Nother's Theorem of interest:

http://en.wikipedia.org/wiki/Nöther's_theorem

where different symmetries are shown to underly different conservation "laws".

 

[lpetrich]

U(1) is isomorphic to SO(2), the 2D rotation group.

The connection with the polarization of light is that the polarization of massless fields in n space-time dimensions lives in the (n-2) transverse dimensions, in this case, 2. So the transverse-dimension rotation group in 4D is SO(2).

The Lorentz group is indeed SO(3,1) -- the numbers are because the space-time metric's signature is +++- or ---+, depending on the convention.