# Tachyons as a Consequence of Light-Cone Reflection Symmetry

## Abstract

**:**

## 1. Introduction

## 2. VSR

- (1)
- Rotations in the x-y plane;
- (2)
- Boosts in the z direction: $u\to \sigma u;v\to {\sigma}^{-1}v;$
- (3)
- $x\to x+au;v\to v+2ax+{a}^{2}u;$ and
- (4)
- $y\to y+bu;v\to v+2by+{b}^{2}u.$

## 3. LCR

- (1)
- Two $\lambda $ transformations $\to $ a $\lambda $transformation with parameter ${\lambda}_{1}+{\lambda}_{2};$
- (2)
- A $\lambda $ transformation followed by a $\kappa $ transformation $\to $ a $\kappa $ transformation with parameter $\kappa -\lambda ;$
- (3)
- A $\kappa $ transformation followed by a $\lambda $transformation $\to $ a $\kappa $ transformation with parameter $\kappa +\lambda ;$
- (4)
- Two $\kappa $ transformations $\to $a $\lambda $transformation with parameter ${\kappa}_{1}-{\kappa}_{2}.$

## 4. Constructing the Lagrangian

## 5. Properties of the Lagrangian

## 6. Further Gauge Invariance

## 7. Conclusions

^{2}, if we assume the existence of a sterile neutrino with mass of about 1 eV/c

^{2}, for which there is some evidence from short baseline experiments [22].

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Chodos, A.
Tachyons as a Consequence of Light-Cone Reflection Symmetry. *Symmetry* **2022**, *14*, 1947.
https://doi.org/10.3390/sym14091947

**AMA Style**

Chodos A.
Tachyons as a Consequence of Light-Cone Reflection Symmetry. *Symmetry*. 2022; 14(9):1947.
https://doi.org/10.3390/sym14091947

**Chicago/Turabian Style**

Chodos, Alan.
2022. "Tachyons as a Consequence of Light-Cone Reflection Symmetry" *Symmetry* 14, no. 9: 1947.
https://doi.org/10.3390/sym14091947