Grand Unification Theory

G=SU(3)×SU(2)×U(1)

G is gauge group.

Grand unification theory is expansion of G.

We have 4 powers in our nature, which are weak interaction, strong interaction, electromagnetic interaction, and gravity.

The integration is so hard because of gravity. G may need super gravity for expansion. There is no space and time.

SU(5)⊃SU(3)×SU(2)×U(1)

This is corruption of everything, and it must be the beginning.

It is very difficult to capture Zero.

SO(10)⊃SU(5)×U(1)

Higgs field

Now I got φ. There is no matter in Gauge theory, but scalar potential is for gravity.

gσρ(x)→W(x)gσρ(x)

Gravity and Electromagnetic Field are integrated.

However, there are space and time between x and x0. This is against Gauge theory because of General theory of relativity.

Then, Higgs field solved this contradiction.

SU(2)×U(1)

This is called spontaneous symmetry breaking.

Gauge symmetry never be broken, and matter is not Zero.

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.