Here are some questions that have been puzzling me about symmetry and charge. Any answers to any of these questions would be very helpful. Thank you. What does U(1) gauge symmetry mean? Does anyone have a simple explanation? Can Maxwell's equations be derived from the premise of U(1) gauge symmetry? If so, how? Do Maxwell's equations imply U(1) symmetry? Is there an operator to obtain the electric charge of a particle from its quantum state?