Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Integers as a Key to Understanding Quantum Mechanics

Victor Korotkikh, Andrei Yu. Khrennikov

Published Jan 1, 2010• 4 citations
Publisher

Abstract

A description of complex systems based on integers is considered in the paper to suggest a new way of understanding quantum mechanics.
DOI
10.1063/1.3431508

Related papers

The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics

G. Coddens

This paper aims at explaining that a key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R3. In the three-dimensional rotation group, the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding that is acquired to derive the free-space Dirac equation from scratch, proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine’s statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further, we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM.

Symmetry•Apr 12, 2021•4 citations

Can Quantum Mechanics Work Without Imaginary Numbers? A Critical Examination of the Role of Complex Numbers in the Quantum Description of Nature

Ijaz Durrani

•Jan 1, 2026•0 citations

The geometrical meaning of spinors as a key to make sense of quantum mechanics

G. Coddens

This paper aims at explaining that the key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R 4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R 3. In the three-dimensional rotation group the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding acquired to derive the free-space Dirac equation from scratch proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine's statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM.

•Mar 22, 2021•1 citation

Why is quantum physics based on complex numbers?

Felix M. Lev

arXiv:hep-th/0309003•Finite Fields and Their Applications•Sep 15, 2005•19 citations

Why Quantum Mechanics Requires Complex Numbers as Props to Build Its Foundation On

Durrani, Ijaz

•Jan 1, 2025•0 citations

Modeling One-way and Two-way quantum key distribution protocols

Ahmed Mahmoud Sofy, Mohamed Ahmed Shalaby, Hisham Dahshan +1 more

The present cryptography systems security depends on the hardness of factorizing an integer number with a large number of digits to its prime integer factors. In 1994, Peter Shor proposed a quantum procedure (Shor's algorithm) that easily factorizes large integer numbers to its prime factors compared with other algorithms. Consequently, present cryptography systems became endangered and once quantum computers exist, conventional cryptography systems could breakdown. On the other hand, quantum cryptography security is based on the well-known quantum mechanics uncertainty principle, and so the quantum cryptography enhances the cryptography field with a mechanism for eavesdropper detecting. Here, a hardware implementation was proposed for two types of key distribution protocols based on quantum computing, the one-way quantum key distribution protocol (BB84 protocol), and the two-way quantum key distribution protocol.

International Conference on Intelligent Computing and Information Systems (ICICIS)•Dec 1, 2019•3 citations
This paper aims at explaining that a key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R3. In the three-dimensional rotation group, the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding that is acquired to derive the free-space Dirac equation from scratch, proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine’s statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further, we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM.
This paper aims at explaining that the key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R 4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R 3. In the three-dimensional rotation group the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding acquired to derive the free-space Dirac equation from scratch proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine's statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM.
The present cryptography systems security depends on the hardness of factorizing an integer number with a large number of digits to its prime integer factors. In 1994, Peter Shor proposed a quantum procedure (Shor's algorithm) that easily factorizes large integer numbers to its prime factors compared with other algorithms. Consequently, present cryptography systems became endangered and once quantum computers exist, conventional cryptography systems could breakdown. On the other hand, quantum cryptography security is based on the well-known quantum mechanics uncertainty principle, and so the quantum cryptography enhances the cryptography field with a mechanism for eavesdropper detecting. Here, a hardware implementation was proposed for two types of key distribution protocols based on quantum computing, the one-way quantum key distribution protocol (BB84 protocol), and the two-way quantum key distribution protocol.