# A Study of Entangled Systems in the Many-Body Signed Particle Formulation of Quantum Mechanics

## TL;DR

This paper extends a novel signed particle formulation of quantum mechanics to many-body systems, demonstrating its equivalence to the Wigner Monte Carlo method and exploring entanglement dynamics under dissipation.

## Contribution

It introduces a many-body extension of the signed particle approach, providing a natural framework for analyzing entangled systems within this formulation.

## Key findings

- The extended theory is equivalent to the many-body Wigner Monte Carlo method.
- Entanglement is modeled using Gaussian wave packets in the new framework.
- Dissipative backgrounds influence entanglement dynamics.

## Abstract

Recently a new formulation of quantum mechanics has been introduced, based on signed classical field-less particles interacting with an external field by means of only creation and annihilation events. In this paper, we extend this novel theory to the case of many-body problems. We show that, when restricted to spatial finite domains and discrete momentum space, the proposed extended theory is equivalent to the time-dependent many-body Wigner Monte Carlo method. In this new picture, the treatment of entangled systems comes naturally and, therefore, we apply it to the study of quantum entangled systems. The latter is represented in terms of two Gaussian wave packets moving in opposite directions. We introduce the presence of a dissipative background and show how the entanglement is affected by different (controlled) configurations.