# Noether’s Theorem in Non-Local Field Theories

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## Abstract

**:**

## 1. Introduction

## 2. Symmetries and the Conserved Currents

## 3. Non-Local Charged Scalar Field

#### 3.1. Time-Like Components

#### 3.2. Vector Current

#### 3.3. Energy-Momentum Tensor

#### 3.4. Angular Momentum Tensor

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CPT symmetry | Charge, parity, and time reversal symmetry |

QCD | quantum chromodynamics |

T product | time-ordered product |

## Appendix A. Field Derivatives

## Appendix B. Series Summation

## Appendix C. Vector Current from the Minimal Substitution

## References

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Krivoruchenko, M.I.; Tursunov, A. Noether’s Theorem in Non-Local Field Theories. *Symmetry* **2020**, *12*, 35.
https://doi.org/10.3390/sym12010035

**AMA Style**

Krivoruchenko MI, Tursunov A. Noether’s Theorem in Non-Local Field Theories. *Symmetry*. 2020; 12(1):35.
https://doi.org/10.3390/sym12010035

**Chicago/Turabian Style**

Krivoruchenko, Mikhail I., and Arman Tursunov. 2020. "Noether’s Theorem in Non-Local Field Theories" *Symmetry* 12, no. 1: 35.
https://doi.org/10.3390/sym12010035