Nilpotent Fuzz

TL;DR

This paper introduces a novel formalism with commutative nilpotent variables, offering a new classical realization of the Pauli exclusion principle through a generalized nilpotent mechanics framework.

Contribution

It proposes a formalism with commutative nilpotent variables, contrasting supermathematics, and illustrates it with a simple nilpotent oscillator model.

Findings

Formalism with commutative nilpotent variables developed

Illustrated through a simple nilpotent oscillator model

Provides a new classical perspective on the Pauli exclusion principle

Abstract

We present a construction of the formalism where fundamental variables are nilpotent, but in contrast to the supermathematics, commutative. This gives another possibility to realize classically the Pauli exclusion principle. We sketch the relevant formalism and discuss simple model of the nilpotent oscillator to illustrate the generalized nilpotent mechanics.