# Physical Mechanisms Underpinning the Vacuum Permittivity

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## Abstract

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## 1. Introduction

## 2. A Dielectric Model of Vacuum Polarization

## 3. Vacuum Polarization in QED

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Vacuum Fluctuations as Harmonic Oscillators

## References

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**Figure 1.**Cartoon view of the particle-antiparticle (denoted by “+” and “−”) pairs continually created in the vacuum. The arrows indicate the trajectories of the corresponding particles. See text for more details.

**Figure 2.**Vacuum polarization in the one-loop approximation. The wavy lines represent an electromagnetic field ($\gamma $), while a vertex represents the interaction of the field with the fermions (electron–positron pair, ${e}^{-}{e}^{+}$), represented by the loop.The arrows notify the momentum being opposite for particle (electron) and antiparticle (positron). The resulting polarization is maximal for a free electromagnetic field, for which the angular frequency, $\omega =\left|\mathbf{k}\right|c$, with $\mathbf{k}$ the wave vector and c denoting the speed of light.

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**MDPI and ACS Style**

Leuchs, G.; Hawton, M.; Sánchez-Soto, L.L.
Physical Mechanisms Underpinning the Vacuum Permittivity. *Physics* **2023**, *5*, 179-192.
https://doi.org/10.3390/physics5010014

**AMA Style**

Leuchs G, Hawton M, Sánchez-Soto LL.
Physical Mechanisms Underpinning the Vacuum Permittivity. *Physics*. 2023; 5(1):179-192.
https://doi.org/10.3390/physics5010014

**Chicago/Turabian Style**

Leuchs, Gerd, Margaret Hawton, and Luis L. Sánchez-Soto.
2023. "Physical Mechanisms Underpinning the Vacuum Permittivity" *Physics* 5, no. 1: 179-192.
https://doi.org/10.3390/physics5010014