A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

<div style="text-align: center; margin-left: auto; margin-right: auto;">$$ \text{SU}(3) \text{ (color)} \times \text{SU}(2) \text{ (weak isospin)} \times \text{U}(1) \text{ (weak hypercharge)}$$</div>  

Which breaks down to \(\text{SU}(3) \times \text{U}(1)\), where the broken \(\text{U}(1)\) is the electromagnetic symmetry. This equation is also a curvature equation—the corresponding equation—and it says that this time, the curvature of an auxiliary structure known as a gauge potential, when differentiated in a particular way is equal, again, to the amount of stuff in the system that is not directly involved in the left-hand side of the equation. So it has many similarities to the above equation, both involve curvature. One involves a projection, or a series of projections. The other involves a differential operator.