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# The intrinsic method

**The document: ****ISBN 978-2-36923-084-7**** **(extern link).

**The intrinsic method**

It is a mathematical tool to get answers to the so-called (E) question in any three-dimensional space: “Consider a deformed cross product (DCP) in E(3, K) where, usually, K represents either R or C. Consider the image of that DCP in the dual space E*(3, K) of E(3, K). How can I divide it and get a pair ([P], **z**) in M(3, K) x E(3, K)?”

**Applications **

**In mathematics**

- Alone, this method is incomplete. It does not give indications on the residual part of the decomposition (see
**the semantic**). Therefore, it must be confronted with the results of the**extrinsic method**. This work has been done and can be read on the French part of the website:**Entre les produits**. - The main part resulting from the intrinsic method differs from the trivial decomposition and the hiatus is per se motivating a discussion.
- A part of that discussion is exposed in “Introducing
**a new vision for the cosmology**”. - In fact, I have pushed the investigation further in the document “
**Einstein-Rosen revisited**”. It turns out that the discussion around the hiatus is a mathematical and technical discussion asking our manner to measure differences.

**In physics**

Despite of its incompleteness, I have applied this method in diverse domains. It gives some interesting information on well-known situations:

- A link between the picture of strings in elongation and the equation of state for the empty regions of our universe: “
**Vacuum and strings**”. - The existence of a volumetric density of force in vacuum: “
**Maxwell’s equations for electromagnetic fields in vacuum****”**. - A hint on the masses inside lattices: “
**Electrons in a lattice**(also called Bloch’s electrons)”. - A direct coincidence between the determinant of the main part and the square of the momentum in Minkowski geometry: “
**The Klein**-**Gordon equation”**. - The possibility to build the first stones of a quantum theory with the main part of some non-trivial decomposition; with application in cosmology: “
**The Tully-Fisher law as quantum gravitational effect?”**(on Zenodo.org).

None of these investigations are definitive since they all are developed in a limited three-dimensional environment and because they should all be confronted with the extrinsic method. It is highly recommended to countercheck them yourself. Discussions are welcome; just **contact** me via the electronic form.

© Thierry PERIAT.

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