# Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

## Abstract

**:**

## 1. Introduction

## 2. Violation of Chiral Symmetry

## 3. Model with a Domain Wall

#### 3.1. Dirac Equation in the Model with a Domain Wall

#### 3.2. Vacuum Energy and Induced Current

## 4. Two-Fermion Model with a Compact Dimension

#### 4.1. Effective Potential of the Model

#### 4.2. Induced Current

## 5. Induced Current in a Model with a Compact Dimension

#### 5.1. Model in (4 + 1)-Dimensional Spacetime

#### 5.2. Model in (2 + 1)-Dimensional Spacetime

## 6. Induced Current in a Planar Model with a Thin Solenoid

## 7. Summary and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Induced current as a function of a at the critical point $m=0$ for various values of the compactification radius R. Induced current vanishes at $aR=n/2$.

**Figure 2.**Induced current as a function of a at the critical point $m=0$ for various values of the compactification radius R. The induced current vanishes at $aR=n/2$.

**Figure 4.**Induced current as a function of m for various values of compactifications radius and fixed value of $\nu $.

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**MDPI and ACS Style**

Zhukovsky, V.C.
Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension. *Symmetry* **2021**, *13*, 210.
https://doi.org/10.3390/sym13020210

**AMA Style**

Zhukovsky VC.
Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension. *Symmetry*. 2021; 13(2):210.
https://doi.org/10.3390/sym13020210

**Chicago/Turabian Style**

Zhukovsky, Vladimir Ch.
2021. "Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension" *Symmetry* 13, no. 2: 210.
https://doi.org/10.3390/sym13020210