# Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II

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## Abstract

**:**

## 1. Introduction

## 2. MHS Theory

#### 2.1. MHS Local Symmetry and MHSYM Model

#### 2.2. Gauge Sector: MHSYM Model

#### 2.3. Matter Sector

#### 2.3.1. Minimal Matter: Spacetime Fields

#### 2.3.2. Master Field Matter in Adjoint Representation

#### 2.3.3. Master Field Matter in the Fundamental Representation. I

#### 2.3.4. Master Field Matter in the Fundamental Representation. II

## 3. Spacetime Description

#### 3.1. Spacetime Fields and the Free Action

#### 3.2. MHSYM 3-Vertex in Spacetime Description

## 4. Calculation of Amplitudes

#### 4.1. Minimal Spacetime Matter

#### 4.1.1. Feynman Rules

#### 4.1.2. Example: Four-Point Amplitude

#### 4.2. Master Space Matter in the Fundamental Representation

#### 4.2.1. Feynman Rules

#### 4.2.2. Example: Four-Point Amplitude

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Properties of the Moyal Product

## Appendix B. Hermite Basis

## Appendix C. Further Hermite Basis

#### Appendix C.1. Notation

#### Appendix C.2. Moyal Commutator in Hermite Basis

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**MDPI and ACS Style**

Cvitan, M.; Prester, P.D.; Giaccari, S.G.; Paulišić, M.; Vuković, I.
Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II. *Symmetry* **2021**, *13*, 1581.
https://doi.org/10.3390/sym13091581

**AMA Style**

Cvitan M, Prester PD, Giaccari SG, Paulišić M, Vuković I.
Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II. *Symmetry*. 2021; 13(9):1581.
https://doi.org/10.3390/sym13091581

**Chicago/Turabian Style**

Cvitan, Maro, Predrag Dominis Prester, Stefano Gregorio Giaccari, Mateo Paulišić, and Ivan Vuković.
2021. "Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II" *Symmetry* 13, no. 9: 1581.
https://doi.org/10.3390/sym13091581