U(1) rotates 2D complex values. SU(2) rotates real 3D vectors. SU(3) rotates complex 3D vectors. SU(3) combines 2D phase rotations internal to each component with 3D rotations that mix components. What, if anything, makes U(1) × SU(2) distinct from SU(3)?
-
In guessing the action, it turns out to be really helpful to include symmetries. Some obvious ones are translation and rotation. But you can also have “rotations” in the space of values (which the field gets sent to). And local means you can rotate them differently at different..
Points in spacetime. By assuming this symmetry you get accompanying gauge fields. In short, the group acts on the “matter field” (e.g. electron field) by rotating its value. The gauge field keeps track of the different rotations at different points. And they describe reality.
