# Stochasticity, topology, and spin

## TL;DR

This paper introduces a novel approach to quantum mechanics by transforming the complex Schrödinger equation into spinor or coupled scalar field equations, emphasizing stochasticity, topology, and spin as a topological invariant.

## Contribution

It presents a new formalism replacing the imaginary unit with a matrix, linking stochasticity and topology to spin and mass in quantum systems.

## Key findings

- Reformulation of Schrödinger equation using matrix substitution
- Spin as a topological invariant in stochastic quantum models
- Mass potentially arising from stochastic processes

## Abstract

Complex Schroedinger equation is transformed to spinor or coupled scalar field equations replacing the imaginary unit $i$ by a matrix $\begin{bmatrix} 0 & 1 \\-1 & 0 \end{bmatrix}$. New perspecive on stochasic approach is developed with spin as topological invariant and mass having stochastic origin in this Spinor Random Field formalism.