# Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology

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## Abstract

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## 1. Introductory Review of Dressed Photon Technology

#### 1.1. Broad Overview

**Five conventional common views in optics**

**I.**- Light is a propagating wave that fills a space. Its spatial extent (size) is much larger than its wavelength.
**II.**- Light cannot be used for imaging and fabrication of sub-wavelength-sized materials. Furthermore, light cannot be used for assembling and operating sub-wavelength-sized optical devices.
**III.**- For optical excitation of an electron, the photon energy must be equal to or higher than the energy difference between the relevant two electronic energy levels.
**IV.**- An electron cannot be optically excited if the transition between the two electric energy levels is electric dipole forbidden.
**V.**- Crystalline silicon has a very low light emission efficiency and is thus unsuitable for use as an active medium in light-emitting devices.

#### 1.2. Nanofabrication Technology and the Size of a DP

#### 1.2.1. Photochemical Vapor Deposition

#### 1.2.2. Smoothing Material Surfaces

## 2. New Theory for Dressed Photon

#### 2.1. Missing Aspect of Quantum Field Interaction Theory

#### 2.2. Augmented Maxwell’s Equation

## 3. Quantization of the Clebsch Dual Field and DP Model

## 4. Connection with Cosmology

**Stage I analyses**

**Stage II analyses**

## 5. Methods: Formulation of the Clebsch Dual Field

**Category I.**

**Category II.**

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical experimental setups for creating a DP. (

**a**) on a nanoparticle; (

**b**) on the tip of a fiber probe; (

**c**) on bumps of a rough material surface; (

**d**) on doped atoms in a host crystal.

**Figure 3.**Ratio of the standard deviation of the roughness of a plastic PMMA surface before and after etching. The downward arrow represents the value of l that is equal to ${\lambda}_{in}$. The width of the grey band corresponds to the maximum size of the DP. The ratio ${\sigma}_{after}/{\sigma}_{before}$ was derived from the values of ${\sigma}_{before}$ and ${\sigma}_{after}$ given in Figure 4 of Ref. [15].

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**MDPI and ACS Style**

Sakuma, H.; Ojima, I.; Ohtsu, M.; Ochiai, H.
Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology. *Symmetry* **2020**, *12*, 1244.
https://doi.org/10.3390/sym12081244

**AMA Style**

Sakuma H, Ojima I, Ohtsu M, Ochiai H.
Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology. *Symmetry*. 2020; 12(8):1244.
https://doi.org/10.3390/sym12081244

**Chicago/Turabian Style**

Sakuma, Hirofumi, Izumi Ojima, Motoichi Ohtsu, and Hiroyuki Ochiai.
2020. "Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology" *Symmetry* 12, no. 8: 1244.
https://doi.org/10.3390/sym12081244