# Scattering in Geometric Approach to Quantum Theory

## Abstract

**:**

## 1. Introduction

## 2. Geometric Approach

## 3. Elementary Excitations

ASSUMPTION. We assume that collections $({f}_{1},\dots ,{f}_{n})$ of non-overlapping functions are dense in ${}^{n}={\mathcal{S}}^{mn}$

**Lemma**

**1.**

## 4. Scattering Møller Matrices

**Lemma**

**2.**

**Lemma**

**3.**

**Theorem**

**1.**

**Lemma**

**4.**

**Theorem**

**2.**

## 5. Inclusive Scattering Matrix

**Theorem**

**3.**

## 6. Analogs of Green Functions

## 7. Discussion

_{i}: $\to End\left(\mathcal{L}\right)$ can be used to define the $in$-state and

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | We say that a closed convex set $\mathcal{C}$ is a convex cone if for every point $x\in \mathcal{C}$ all points of the form $\lambda x$ where $\lambda $ is positive also belong to $\mathcal{C}.$ Notice that in our terminology a vector space is a convex cone. |

2 | |

3 | Notice that (16) and (17) can be considered either as an inclusive scattering matrix of elementary excitations of state $\omega $ or as an inclusive scattering matrix of elementary excitations of state $\alpha $. A similar statement is true for analogs of green functions introduced in Section 6. It is not clear whether this strange duality has any physical meaning. |

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Schwarz, A. Scattering in Geometric Approach to Quantum Theory. *Universe* **2022**, *8*, 663.
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Schwarz A. Scattering in Geometric Approach to Quantum Theory. *Universe*. 2022; 8(12):663.
https://doi.org/10.3390/universe8120663

**Chicago/Turabian Style**

Schwarz, Albert. 2022. "Scattering in Geometric Approach to Quantum Theory" *Universe* 8, no. 12: 663.
https://doi.org/10.3390/universe8120663