# The-Klein-Gordon-Equation

Go back to the “Starting page”.

**Title: **New analysis of the Klein-Gordon equation within the theory of deformed cross products, versus 2021, (not yet stabilized).

**Matriculation**: ISBN 978-2-36923-079-3, EAN 9782369230793.

**Language**: GB/USA.

**Published**: 30 September 2021.

**Number of pages**: 8.

**Document**: 079 3 gb intro (283.71 Ko).

**Résumé:** The Klein-Gordon equation describing the propagation of massive waves is currently analyzed with Dirac's ideas and works. His equation and his matrices are strategic tools for everyone studying the standard model for particles. The initial goal of this document is to propose an alternative analysis for that crucial equation and to explore the consequences of this proposition. Within that approach, the Euclidean geometry of our everyday world reveal unexpected visages; for example, isotropic wave vectors and positions must be introduced into the debate. This document suggests a mechanism for the discovery of masses carried by these waves and initiates a procedure for the quantification of the area metrics.

**Context:**

The Klein-Gordon equation certainly is one of the most fascinating and interesting equation in physics. It not only explains how massive wave propagates. It also is in some manner the “mother” of Dirac’s equation which is so important in particle physics.

## Another consequence of the initial theorem:

The first part of the document exposing the intrinsic method ends with the so-called “initial theorem”. Concretely, this theorem affirms that if a deformed cross product can be non-trivially decomposed, then its decomposition is associated with at least one polynomial of degree two depending on the components of the projectile (first argument - see the semantic) involved in that deformed cross product.

This is a very general mathematical result and the starting point for numerous applications of the intrinsic method. Indeed, up to now, any polynomial of degree two depending on the components of some three-dimensional vector is potentially signing the existence of a whole family of deformed cross products.

Since any polynomial of degree two depending on the components of some four-dimensional vector can always be reformulated in a 3 + 1 manner, the initial theorem has many applications in physics. The Klein-Gordon equation is one of them.

This opportunity does not appear immediately. It is merely the result of an inverse logical analysis of my seminal work concerning the non-trivial decompositions of deformed cross products with the help of an intrinsic method.

I improve this way of thinking in the above document. It is the starting point of a series:

1. Part I - Introduction: see above.

2. Dispersion relation for the light in vacuum, please consider the French version.

3. Part II - Fundamental identifications - in revision, please consider the French version.

4. Part III - Tools for a quantization:

Quantification isbn 079 3 (424.26 Ko), 25 october 2021, 25 pages.

This work allows to go further; please consider the exploration on zenodo.org: The Tully-Fisher law.

5. Part IV - Complements on the K.G.E - in revision.

**Author**: Thierry PERIAT.

Go to the page: "Hodge's star operator representations".

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Date de dernière mise à jour : 21/02/2022