# Bulletin of the American Physical Society

# APS March Meeting 2023

## Volume 68, Number 3

##
Las Vegas, Nevada (March 5-10)

Virtual (March 20-22); Time Zone: Pacific Time

### Session YY06: V: General Physics II

10:00 AM–12:00 PM,
Wednesday, March 22, 2023

Room: Virtual Room 6

Chair: Dominic Alfonso, National Energy Technology Laboratory

### Abstract: YY06.00001 : Cohomology of the Generalized Newton's Laws Manifolds

10:00 AM–10:12 AM

#### Presenter:

Zhi an Luan

(University of British Columbia)

#### Author:

Zhi an Luan

(University of British Columbia)

#### Collaboration:

Zhi-An Luan

_{B}) as a kernel of the Generalized Newton's Laws, where G- Newton's Gravity Constant G=2/3 = 0.666 666...; h- Reduced Planck Constant = 2π√3 = 1.088279619x 10 ...; Boltzmann Constant k

_{B}= 8√3 = 1.385640646 ... . Above three fundamental constants as exact non-dimensional monodromy varieties have deep importances in theoretical physics. I also found that gcd(h, k

_{B}) = gcd (2π√3, 8√3) = 2√3, which is a projection P

^{1}in classical Fano manifolds. This paper will cast new extended Fano complex 2-d manifolds based on an important fact: the first natural sheaves are constant sheaves. These all three classical constants: G, h, k

_{B}recast as real constant sheaves such as G

_{i}, h

_{i}, k

_{Bi }i = 1,2,3, ..., such that the Boltzmann sheaves k

_{B}

^{n}=2√3 × n, where integer n = 1,2,3,4, ... ∞; the Planck sheaves h

^{μ}=2π × μ, where real numbers

μ = 0, √n

^{-1}, ... √5

^{-1}, √3

^{-1}, 1=Id, √3, √5, ... √n ... ∞.

Theorem 1. Using Courant Algebroid (CA), there exist an important isomorphic map - circle boundary length l = 2√3×n× tan(π/n)|

_{n→∞}= 2π√3 = h

^{μ=}

^{√3}= h reduced Planck Constant.

I give out all energy deformation retract with coherent sheaves of the Planck Constant. Instead of working with functions of the energy, I define a new coordinate z by

z

^{2}= - E, where real z corresponds to the "forbidden" region of negative E. In fact this z is just the r

_{coh}variety in the Generalized Newton's Laws, and r

_{coh}

^{2 }is just the speed V. Hence the representation of momentum can be showed as extended Planck sheaves h

^{z}= 2π × z = 2π × r

_{coh}, such that, sequences 2π√0, 2π√5

^{-1}, 2π√3

^{-1}, 2π×1, 2π√3, 2π√5, ... ,2π√n=∞. Using these geometry data and the Courant Algebroid with extended Dirac operators TX + T

^{*}X in a maximal complex torus, I give follow second result:

Theorem 2. The Planck Constant sheaves have important deformation retract form:

{2n ± √3 + (2n ± √3)

^{-1}} |

_{n=1}= 4; {2n ± √5 - (2n ± √5)

^{-1}}|

_{n=1}=4. Then the maximal limit light speed is 4 rather than c =3...km/s.

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