# Scattering in Algebraic Approach to Quantum Theory—Associative Algebras

## Abstract

**:**

## 1. Introduction

## 2. Scattering Matrix

**Lemma**

**1.**

**Definition**

**1.**

**Lemma**

**2.**

**Assumption**

**1.**

**Theorem**

**1.**

## 3. LSZ Formula

## 4. Inclusive Scattering Matrix

## 5. Fermions

## 6. BRST Formalism

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | The spatial and time translations are naturally defined for a theory in $(d+1)$-dimensional flat space-time. Notice that we do not assume that we consider such a a theory. For example we can consider a theory on $(d+2)$-dimensional anti de Sitter space; the symmetry group of this space has a $(d+1)$-dimensional commutative subgroup that can be interpreted as a group of time and spatial translations. In string field theory we can interpret time and spatial translations as transformations of the target. |

2 | It is possible that the “elementary space” $\mathfrak{h}$ does not describe all particles existing in the theory (for example, we are missing some composite particles). In this case we have a chance to get a theory with particle interpretation extending the space $\mathfrak{h}.$ |

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Schwarz, A. Scattering in Algebraic Approach to Quantum Theory—Associative Algebras. *Universe* **2022**, *8*, 660.
https://doi.org/10.3390/universe8120660

**AMA Style**

Schwarz A. Scattering in Algebraic Approach to Quantum Theory—Associative Algebras. *Universe*. 2022; 8(12):660.
https://doi.org/10.3390/universe8120660

**Chicago/Turabian Style**

Schwarz, Albert. 2022. "Scattering in Algebraic Approach to Quantum Theory—Associative Algebras" *Universe* 8, no. 12: 660.
https://doi.org/10.3390/universe8120660