# Particle Production in Strong Electromagnetic Fields and Local Approximations

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## Abstract

**:**

## 1. Introduction

## 2. External Field Configuration. Turning Points

## 3. Locally Constant Field Approximation

#### 3.1. Momentum Distributions

#### 3.2. Total Number of Pairs

## 4. Quantum Kinetic Equations

## 5. Results

#### 5.1. Momentum Distributions for Positive $\sigma $

#### 5.2. Negative $\sigma $. Interference Effects

#### 5.3. Total Number of Particles

## 6. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

QED | Quantum electrodynamics |

LCFA | Locally constant field approximation |

QKE | Quantum kinetic equations |

TP | Turning point |

## References

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**Figure 1.**Temporal dependence of the external field Equation (1) (dashed lines) and vector potential Equation (2) (solid lines) in the case of positive (

**left**) and negative (

**right**) values of the parameter $\sigma $. In the latter case, the vector potential is not monotonous, so the classical electron trajectory can have two turning points.

**Figure 2.**Momentum distributions of negatively charged fermions and bosons produced in the external field Equation (1). The transverse momentum component is ${\mathit{p}}_{\perp}=0$. The solid lines represent the exact results obtained by means of the QKE. The dashed lines correspond to the LCFA Equation (8) and LDA Equation (22) for fermions. The field parameters are $E=0.5{E}_{\mathrm{c}}$, $\sigma =1/2$, $\tau =5{m}^{-1}$, $\delta =10$ (

**left**panel) and $E={E}_{\mathrm{c}}$, $\sigma =1/2$, $\tau =3{m}^{-1}$, $\delta =10$ (

**right**panel).

**Figure 3.**Momentum distribution of negatively-charged fermions and bosons produced in the external field (1) with $E=3{E}_{\mathrm{c}}$, $\sigma =-1/2$, $\tau =2{m}^{-1}$, and $\delta =10$. The transverse momentum component is ${\mathit{p}}_{\perp}=0$. In the right panel, we also display the approximate spectra obtained by means of the LCFA (10) and LCFA+ (11) (“B” and “F” stand for bosons and fermions, respectively).

**Figure 4.**(

**left**) Total number of pairs per unit volume produced in a combination of two Sauter pulses Equation (1) with $\sigma =-1/2$, $\tau =4{m}^{-1}$, and $\delta =10$ in the case of bosons and fermions together with the LCFA prediction Equation (14); (

**right**) Ratio of the total particle yields in the case of bosons and fermions as a function of the field amplitude E and the estimate R evaluated according to Equation (24).

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**MDPI and ACS Style**

Aleksandrov, I.A.; Sevostyanov, D.G.; Shabaev, V.M.
Particle Production in Strong Electromagnetic Fields and Local Approximations. *Symmetry* **2022**, *14*, 2444.
https://doi.org/10.3390/sym14112444

**AMA Style**

Aleksandrov IA, Sevostyanov DG, Shabaev VM.
Particle Production in Strong Electromagnetic Fields and Local Approximations. *Symmetry*. 2022; 14(11):2444.
https://doi.org/10.3390/sym14112444

**Chicago/Turabian Style**

Aleksandrov, Ivan A., Denis G. Sevostyanov, and Vladimir M. Shabaev.
2022. "Particle Production in Strong Electromagnetic Fields and Local Approximations" *Symmetry* 14, no. 11: 2444.
https://doi.org/10.3390/sym14112444