#
Quantum Mechanics as Hamilton–Killing Flows on a Statistical Manifold^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Some Background

## 3. Hamiltonian Flows

#### 3.1. hE Symplectic Form

#### 3.2. Hamilton’s Equations and Poisson Brackets

#### 3.3. The Normalization Constraint

## 4. The Information Geometry of E-Phase Space

#### 4.1. The Metric on the Embedding E-Phase Space ${T}^{*}{S}^{+}$

#### 4.2. A Complex Structure for ${T}^{*}{S}^{+}$

#### 4.3. The Metric Induced on the E-Phase Space ${T}^{*}S$

#### 4.4. Refining the Choice of Cotangent Space: Complex Coordinates

## 5. Hamilton–Killing Flows

## 6. Hilbert Space

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

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Caticha, A.
Quantum Mechanics as Hamilton–Killing Flows on a Statistical Manifold. *Phys. Sci. Forum* **2021**, *3*, 12.
https://doi.org/10.3390/psf2021003012

**AMA Style**

Caticha A.
Quantum Mechanics as Hamilton–Killing Flows on a Statistical Manifold. *Physical Sciences Forum*. 2021; 3(1):12.
https://doi.org/10.3390/psf2021003012

**Chicago/Turabian Style**

Caticha, Ariel.
2021. "Quantum Mechanics as Hamilton–Killing Flows on a Statistical Manifold" *Physical Sciences Forum* 3, no. 1: 12.
https://doi.org/10.3390/psf2021003012