The conservation of charge relates to the mathematical statement of a vanishing divergence of the charge current. Study an example:  the conservation of charge for a complex wave function. Conservation of charge can be derived using the infinitesimal change of phase of a complex wave function.

By “conserved” a physicist means there exists a current, conserved quantity and a continuity equation for the current and charge.

Isotopic spin has three components.
Study the relation between the energy and momentum of a particle.

1. Inertial Reference Frames
2. Principle of Least Action
3. Invariance of the Laws of Nature
4. Lagrangian Mechanics
5. Conservation of Charge and Momentum
6. Relativistic Wave Equation and Conservation Laws
7. Invariance under Gauge Transformations
8. Gauge Theory

This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. The course is taught by Leonard Susskind, the Felix Bloch Professor of Physics at Stanford University.