For the electron, you were just taking one direction of rotation, and that is called U1. For the quarks, you have three different axes and the rotations you do are called SU3. How can you describe the value of a vector at one point in space compared to the value at another point? You need to carry it, and you need a field to tell you how to carry it. These fields are called connection fields for obvious reasons,. They help you connect one point to another, they are also called gauge fields.

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