# Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem

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## Abstract

**:**

## 1. Introduction

## 2. A Pseudo-Unitary Representation

#### 2.1. Motivation

#### 2.2. Operator Representations and Fock States with Hermite Polynomials

#### 2.3. Transformation Properties under the Lorentz Boosts

#### 2.4. The Pseudo-Unitary Inner Product or Invariant Bilinear Functional

## 3. Fock States as Representations of Lorentz Symmetry

## 4. Discussions on Issues of Interpretations

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. List of Explicit Relations between Some of the Fock States and the $\left|\mathit{n};\mathit{c};\mathit{j},\mathit{m}\right.\u232a$ Basis States of $\mathit{S}\mathit{O}(\mathbf{1},\mathbf{3})$ Irreducible Representations

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**MDPI and ACS Style**

Bedić, S.; Kong, O.
Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem. *Symmetry* **2020**, *12*, 39.
https://doi.org/10.3390/sym12010039

**AMA Style**

Bedić S, Kong O.
Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem. *Symmetry*. 2020; 12(1):39.
https://doi.org/10.3390/sym12010039

**Chicago/Turabian Style**

Bedić, Suzana, and Otto Kong.
2020. "Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem" *Symmetry* 12, no. 1: 39.
https://doi.org/10.3390/sym12010039