# Dispersion Forces Between Fields Confined to Half Spaces

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## Abstract

**:**

## 1. Introduction

## 2. Scalar Field Confined to Half Spaces and the Casimir Effect

#### 2.1. The Model

#### 2.2. Transition to $TGTG$ Formula

## 3. Polarization Operator in Half Space

## 4. Vacuum Energy

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The factor $\mathcal{N}$ playing the role of the reflection coefficient of the half space as a function of momenta $\gamma $, $m=1,\lambda =1$.

**Figure 2.**The ratio, $\eta $, of the Casimir energy of Equation (61) and the Casimir energy of the massless scalar field with Dirichlet boundary conditions on the plates. $\eta $ is drawn in logarithmic scale as a function of dimensionless separation $\lambda L$ for different vales of $\mu =m/\lambda $. From top to bottom, $\mu =0.001,0.01,0.5,1$.

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**MDPI and ACS Style**

Bordag, M.; Pirozhenko, I.G.
Dispersion Forces Between Fields Confined to Half Spaces. *Symmetry* **2018**, *10*, 74.
https://doi.org/10.3390/sym10030074

**AMA Style**

Bordag M, Pirozhenko IG.
Dispersion Forces Between Fields Confined to Half Spaces. *Symmetry*. 2018; 10(3):74.
https://doi.org/10.3390/sym10030074

**Chicago/Turabian Style**

Bordag, M., and I.G. Pirozhenko.
2018. "Dispersion Forces Between Fields Confined to Half Spaces" *Symmetry* 10, no. 3: 74.
https://doi.org/10.3390/sym10030074