# From Micro to Macro: A Relativistic Treatment of the Chiral Energy Shifts Caused by Static Electromagnetic Effects on Free Electrons

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## Abstract

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## 1. Introduction

## 2. Preliminary Details

## 3. Results

## 4. Discussion and Conclusions

## 5. Methods

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Expectation values of energy shifts due to electromagnetic potentials ${A}_{\mu}$. The energy shift expectation values, computed in the single-electron state $\left|\mathsf{\Psi}(\overrightarrow{k})\right.\u232a={\lambda}_{+}\left|\uparrow ,\overrightarrow{k}\right.\u232a+{\lambda}_{-}\left|\downarrow ,\overrightarrow{k}\right.\u232a$, have been normalized by $\left|e\right|\overline{A}$, with $\overline{A}={A}_{0}={A}_{1}={A}_{2}={A}_{3}$. Dimensionless results for the fully relativistic treatment $\u2329{\Delta}_{{A}_{\mu}}\mathcal{H}\u232a$ (blue), non-relativistic limit (NRL) achiral state $\u2329{\Delta}_{{A}_{\mu}}{\mathcal{H}}_{NRL}^{\mathrm{achir}}\u232a$ (orange), and NRL completely polarized states $\u2329{\Delta}_{{A}_{\mu}}{\mathcal{H}}_{NRL}^{\mathrm{pol},\phantom{\rule{4.pt}{0ex}}\mathrm{R}}\u232a$ (yellow) and $\u2329{\Delta}_{{A}_{\mu}}{\mathcal{H}}_{NRL}^{\mathrm{pol},\phantom{\rule{4.pt}{0ex}}\mathrm{L}}\u232a$ (purple) are presented as functions of the electron momentum $|\overrightarrow{k}|$, in units of MeV. See the Results for further description of these states, in particular Equations (16)–(20).

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**MDPI and ACS Style**

Kurian, P. From Micro to Macro: A Relativistic Treatment of the Chiral Energy Shifts Caused by Static Electromagnetic Effects on Free Electrons. *Entropy* **2022**, *24*, 358.
https://doi.org/10.3390/e24030358

**AMA Style**

Kurian P. From Micro to Macro: A Relativistic Treatment of the Chiral Energy Shifts Caused by Static Electromagnetic Effects on Free Electrons. *Entropy*. 2022; 24(3):358.
https://doi.org/10.3390/e24030358

**Chicago/Turabian Style**

Kurian, Philip. 2022. "From Micro to Macro: A Relativistic Treatment of the Chiral Energy Shifts Caused by Static Electromagnetic Effects on Free Electrons" *Entropy* 24, no. 3: 358.
https://doi.org/10.3390/e24030358