How Do Symmetries Relate to Conservation Laws in Physics?

[newphy]

I am trying to understand the connection between symmetry and conservation.

For the electromagnetic force, the conserved quantity is charge, the corresponding symmetry is the phase of the wave and the force carrier is the photon.
For the electroweak force, the conserved quantities are the weak isospin and the weak hypercharge (for the weak and em forces) and the force carriers are the W+, W- and Z0. What is the corresponding symmetry?
Same question for the strong force. The conserved quantity is the Isospin and the force carrier is the gluon. What is the symmetry corresponding to this force?

Thanks

 

[samalkhaiat]

I am trying to understand the connection between symmetry and conservation.

For the electromagnetic force, the conserved quantity is charge, the corresponding symmetry is the phase of the wave and the force carrier is the photon.

Which is the invariace under SO(2)=U(1) rotation.

For the electroweak force, the conserved quantities are the weak isospin and the weak hypercharge (for the weak and em forces) and the force carriers are the W+, W- and Z0. What is the corresponding symmetry?

Invariance under SU(2) \times U(1)_{ Y }.

Same question for the strong force. The conserved quantity is the Isospin and the force carrier is the gluon. What is the symmetry corresponding to this force?

Thanks

Not Iso-spin. The invariance under "rotation" in the 3-dimensional Colour space, which form the group SU(3)_{ C }, leads to 8 conserved quantities (called the colour charges) to which the 8-gluons get coupled.