# The intrinsic method

**The document can be discovered on vixra. **

The intrinsic method is a mathematical tool bringing a part of the answer to the so-called (E) question. It only works in any three-dimensional space and, if considered separately from the extrinsic method, it is an incomplete procedure.

Consider a deformed cross product in E(3, K) where, usually, K represents either R or C. Consider the image of that product in the dual space E*(3, K). The question is: “How can I divide it and get a pair ([P], **z**) in M(3, K) x E(3, K) such that |Ù_{A}(**a**, **b**) > = [P].|**b** > + |**z** >?”

**Applications **

**In mathematics**

- Since this method (i) does not give indications on the residual part of the decomposition (see
**the semantic**) and (ii) is yielding a main part [P] differing from the trivial decomposition, it must be confronted with the results of the extrinsic method.

**In physics**

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

- A link between the picture of classical 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 vacuum
**”**. - A hint on the masses inside lattices: “
**Electrons in a lattice**” (also called Bloch’ electrons). - A direct
**The Klein**-**Gordon equation”**. - The possibility to build the first stones of a quantum theory with the main part of some non-trivial decomposition: “The Tully-Fisher law as quantum gravitational effect?
**”**(Document 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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Last edited: 11/02/2021