Effect Algebras Are Not Adequate Models for Quantum Mechanics

Robert Olkiewicz

Anatolij Dvurečenskij

Jincheng Zhang

This paper explores the application of non-associative algebra to the representation and manipulation of quantum state systems. The current mathematical landscape often falls short in adequately capturing the intricate and non-linear entanglement patterns inherent in quantum mechanics. We propose a novel algebraic structure, termed "non-associative entanglement," designed to address these limitations by providing a framework for representing and calculating entanglement with unprecedented precision. The core claim is to establish a new class of non-associative algebras capable of accurately modeling and processing complex quantum states, facilitating automated calculations of entanglement and superposition. This work will detail the mathematical foundations of this approach, showcasing its potential to revolutionize quantum state representation and computation.

K. Kowalski, Jakub Rembieliński, Loucas C. Papaloucas

Abstract. The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra [ ˆ J, U] = U, where U is unitary, which is a direct consequence of the Heisenberg algebra [ˆϕ, ˆ J] = i, but it is more adequate for the study of the circlular motion. Key words: quantum mechanics, coherent states, quantum groups

S. P. Gudder

Franklin E. Schroeck