Gauge Theory

I use fractal as art, but there are some relations with gauge theory.

E is electric field.

∇E=ρ/ε0

∇B=0

B is Magnetic field.

B=∇A

A is vector potential.

∇E=-∂B/∂t

∴

∇(E+∂A/∂t)=0

E+∂A/∂t=-∇φ

φ is scalar potential.

∴

B=∇A, E=-∇φ-∂A/∂t

This is Gauge symmetry, and the potential is chaotic.

φ(x)→φ'(x)=e^iθ*φ(x)

e is Electric charge.