Table-of-contents.

Version FR.

This page is only giving a provisory overview on my work for readers using the English language.

The theory of the (E) question: basic ideas for a new cosmology.

1. Covariance: the origin of the concept in A. Einstein’ master work:

“A starting point for dissertations on covariance, derivations, and propagators”.

2. Mathematical tools.
   1. Confronting E. B. Christoffel’s and E. Cartan’s works.

1. 2. The anti-commutativity.
      1. Classification.

1. 1. 2. Co-homology.

1. 3. Matricial derivations.
      1. Part 01.

1. 1. 2. Part 02.

1. 4. Revisiting E. B. Christoffel’s work.

1. 5. Topology, basics.

1. 6. The Tartaglia-Cardan method.

1. 7. Tetrahedron, Euclid and the concept of surface.

1. 8. Dirac’s equation.

1. 1. The visual analysis of matrices.

1. 10. Matricial roots of minus one in M(4, C).

1. 11. Matricial mothers/hearts (concept).

1. 50. Matricial hearts (extension).

1. 1000. Matricial hearts and particles.

3. Mathematical structures.
   1. Lie algebras.

1. 2. C*-algebras:
      1. naïve version.

1. 1. 2. a deeper analysis.

1. 3. Where is the neutral element?

1. 4. Involution and the dispersion relation for the light propagating in vacuum.

1. 5. The algebraic dynamics.

1. 6. A multiplicative group structure for the matricial hearts representing the particles.

4. Mathematical methods.
   1. Gauss: theorema egregium and the birth of a mathematical question.

“The secret presence of deformed tensor products.”

1. 2. Semantic.

1. 3. Extrinsic method in a two-dimensional space.

1. 4. Extrinsic method in any space.

1. 5. Intrinsic method in a three-dimensional space.

1. 6. Confronting the extrinsic and the intrinsic method in a three-dimensional space with the help of Helmholtz decomposition.

1. 7. Strategic discriminant in a four-dimensional space.

1. 8. The Russian dolls: an unachieved essay.

5. Applications for the extrinsic method.
   1. The dispersion relation and the Klein-Gordon equation.

1. 2. The so-called “gravitational term” in the covariant version of the Lorentz law.

1. 3. Curvature tensor associated with the variations of deformed tensor products.

6. Applications for the intrinsic method.
   1. Reanalyzing the element of length in the ADM formalism – The Euclidean enigma: E. Cartan’s bispinors in the everyday world?

1. 2. Revisiting the Einstein-Rosen proposition (1935).

1. 3. Gravitation and type I supra-conductivity.

1. 4. The kern of the principal part of a decomposition and its transposed matrix as a pair of operators in a quantum dynamical approach - link with the Tully-Fisher law.

7. Cosmology.
   1. Hubble or Hoyle?

1. 2. The dispersion relation for the light propagating in vacuum.

1. 3. The Klein-Gordon equation.

1. 4. Classical elastic strings.

1. 5. The Navier-Stockes equations.

1. 6. The Thirring-Lense effect.

1. 7. Lumine naturea: the light as a spinning flow?

1. 8. Revisiting Maxwell’s vacuum.

1. 1. Lamb and Rutherford unstable vacuum and its link with a C*-algebra.

1. 10. Revisiting Heisenberg:

“Is the uncertainty principle linked to the problematic concerning the horizon?”

1. 11. Einstein versus Heisenberg:

“Preserving c and h in a change of frame”.

1. 1. 1. A new type of electromagnetic fields?

1. 1. 2. The chameleons:

“Do they have a link with the B-modes?”

1. 1. 3. Dual fields:

“The consequences of the Hodge’s operator representations”.

1. 1. 4. The Cauchy problem and the quantum Hall effect. 

8. The covariant formulation of Lorentz law in electromagnetism.
   1. An operator?
      1. Basics-naïve idea (the flat space case).

1. 1. 2. A deeper analysis (in any space).

1. 2. Electromagnetic connections instead of electromagnetic gauge?

1. 3. The golden rule:

“When the inverse of the transposed matrix is the transposed inverse of a given matrix”.

1. 4. Scenario explaining heuristically the type II supra-conduction.

9. The GTR2 approach (or the E. Cartan’s like approach).
   1. Foundations.

1. 2. Studying the variations of the metric from different viewpoints.

1. 3. The concept of geometrical invisibility: can it explain the dark energy?

1. 4. Confrontation with the formulation of the Lorentz law as operator.

© Thierry PERIAT.

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