An Exclusion Principle for Sum-Free Quantum Numbers

TL;DR

This paper introduces a generalized exclusion principle for quantum particles based on sum-free conditions, leading to new insights into quantum many-body systems and a fractal sequence of quantum numbers.

Contribution

It proposes a novel correlated exclusion principle extending fermion and boson principles, with explicit solutions and algebraic structures for quantum operators.

Findings

Derived a sum-free exclusion principle for quantum particles.

Identified a fractal quantum number sequence related to Thue-Thurston sequence.

Established algebraic relations for creation and annihilation operators.

Abstract

A hypothetical exclusion principle for quantum particles is introduced that generalizes the exclusion and inclusion principles for fermions and bosons, respectively: the correlated exclusion principle. The sum-free condition for Schur numbers can be read off as a form of exclusion principle for quantum particles. Consequences of this interpretation are analysed within the framework of quantum many-body systems. A particular instance of the correlated exclusion principle can be solved explicitly yielding a sequence of quantum numbers that exhibits a fractal structure and is a relative of the Thue-Thurston sequence. The corresponding algebra of creation and annihilation operators can be identified in terms of commutation and anticommutation relations of a restricted version of the hard-core boson algebra.