The Generalized Newton's Laws (GNL) - A Complete Conformal Field Theory of Quantum Gravity

This paper will prove that the GNL theory on Quantum Gravity (QG) is a complete and robust Conformal Field Theory (CFT) as the Liouville CFT (LCFT). Here, I will directly from the standard LCFT induce to the complete GNL theory on Quantum Gravity.

(1). Theorem 1.

Let S_L be the Liouville Action functional, in the case of the Riemann sphere, there exists a metric as: e^γφ(z) |dz|² and the law of φ is:

ν(dφ) = e^-S_L ν₀(dφ). (1)

then we can prove that this law is an isomorphism manifold with the Heat Kernel in the Unitary Space-Time of the GNL such as:

Ker= e^-x∗x/(2t)/√2πt. Hence these two CFT theories are an isomorphism map, in topological structures, specially.



(2). Theorem 2.

The LCFT has two parameters γ and μ, is characterized by its central charge:

c_M = 25 - 6 Q² (2)

Q = 2/γ + γ/2. (3)

hence if the central charge c_M = 0 and therefore to

γ = √(8/3) then we induce to a global topology on Quantum Gravity in the GNL:

GM 4(1- M²) = GM 4(1+ M)(1-M) (4)

In normal cases, the Newton's gravity constant G = 2/3 = 0.666..., which leads to

8/3 M(1+ M)(1- M) = Id = 1. (5)

We clearly can use the parameters of the LCFT to lead to the main results on the relation between Mass and Velocity of the GNL:

V = 4(1- M²) = (2cos(φ))²= 4 cos²(φ) (6)

and

M = √(1 - V/4). (7)

(3). Theorem 3.

The GNL is a complele and exact Quantum Gravity theory, since it can give a global dynamics on Expansion and Retraction of the Universe and Fundamental Particle (Using Courant Algebroid):

2 ± √3 + 1/(2 ± √3) = 4. (8)

and

2 ± √5 - 1/(2 ±√5) = 4. (9)

Finally, there exists an ergodic topological form of the quasi-stable light speed v = 3x ... km/s and the limit photon speed v_max= 4:

2n ± √3 + 1/(2n ±√3) ↔ 2n ± √5 - 1/(2n ± √5) (10)