# Plasma-like Description for Elementary and Composite Quantum Particles

## Abstract

**:**

## 1. Introduction

- How can a continuous charge density distribution be approximated by a discrete one with a quantized charge?
- What mathematical model (equations of motion) can underlie such a description?
- How can the description be extended to composite particles?
- What are some implications of the obvious analogy with plasma?

## 2. Methods and Results

#### 2.1. Approximation of a Continuous Charge Density Distribution by a Discrete One with a Quantized Charge

#### 2.2. An Example Mathematical Model

#### 2.3. Extension to Composite Particles

#### 2.4. The Plasma Analogy

## 3. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Electron Coordinates | Positron Coordinates |

−3.1126741447007592777837555796944 | 2.9530344365605025711769473845442 |

−2.8775683647214638678316386267493 | −3.0951381769952591512118001250174 |

−2.6434375832598523581831400447478 | −2.8614098696120820985572576736353 |

−1.9336327385447378036758712466442 | −2.1882892356297157247876068745650 |

−1.6936070421273554090248068336325 | −2.6326516523345556425794778026752 |

−2.1719682464297679903185420586677 | −1.9710273543645197236521756279888 |

−1.4519956803651471460404417607211 | −1.7555235230550466106754786539860 |

−1.2088029171600329445514113518049 | −1.5403236844404032536985003739319 |

−0.96395311532928105718506480243987 | −1.1039117628153018022432733933447 |

−0.71762228955760307445232301075533 | −1.3237515410575950384914085327471 |

−0.47125651467198634491476595790667 | −0.87873421856160715534322966231588 |

−0.22858211104030609796912348102868 | −0.64632138885302414208246702251485 |

0.86186952364267439824952086701953 | 0.33294945631962504080286722164668 |

0.00616783249506095738298247885632 | −0.40611981918357315216289810648891 |

0.23137130395092737580909635004611 | −0.16042959567225122871033380542859 |

0.44789490782808160879397312969880 | 0.08676186721721802846687332761214 |

0.65746934747098210872577876522952 | 0.57756516301030844804631542526482 |

1.2615668189213491342215825540197 | 0.82076073717919350910333838443007 |

1.4597980397241581466451663147530 | 1.3035691589932125510920278727478 |

2.0643955075009215796102922944881 | 2.0187559332910846063814218989366 |

1.6587989484672624969753714473643 | 1.7817077278249609050042692119912 |

1.8599046587703446165936780433590 | 1.5432590795101890022517254564541 |

2.2734402898434140647729061709433 | 2.2542171585208840682836715659146 |

2.7088031793185310430667064345281 | 2.7204794077160776393522523646147 |

2.9363544347316877716974068736781 |

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**Figure 2.**The smooth charge density distribution to be approximated by a collection of discrete quantized charges.

**Figure 3.**The smooth charge density distribution (green) and the discrete charges of the approximating discrete charge density distribution. The charges are mostly arranged in pairs; the clusters of three charges are encircled by ellipses.

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Akhmeteli, A. Plasma-like Description for Elementary and Composite Quantum Particles. *Entropy* **2022**, *24*, 261.
https://doi.org/10.3390/e24020261

**AMA Style**

Akhmeteli A. Plasma-like Description for Elementary and Composite Quantum Particles. *Entropy*. 2022; 24(2):261.
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**Chicago/Turabian Style**

Akhmeteli, Andrey. 2022. "Plasma-like Description for Elementary and Composite Quantum Particles" *Entropy* 24, no. 2: 261.
https://doi.org/10.3390/e24020261