< Looking for a link between GTR and Q(F)T >
December 2009:
September 2009:
August 2009:
SB06GB.pdf [3 pages; 15 August 2009] The string mechanism: an alternative to the Higgs mechanism? I explain my very personal vision.This is a short version of Vide12.pdf. With the help of relatively recent works of Abrikosov, Kleiner and al. concerning supraconducting vortex, I actually develop the strong conviction that my qualitative toy model for supraconductive attostrings proposes an interesting alternative or complementary explaination to the Higgs mechanism. Thierry PERIAT.
SB04GBv2.pdf: explains the differential equations for the componants of the Christoffel's cube in our original approach consisting in a controntation between the metrics induced by the cubes and the connection compatible metrics within a GTR conform approach.
July 2009
SBGB05.pdf: [30 July 2009; 0.529 MB; 2 pages; secured; in English]
The gauge part and the fernionic part of the QCD Lagrangian can be confronted and put on the same foot in SU(3) and in SU(4). This is telling a fundamental interrogation about the interactions between the "matter" and the "field". It is suggesting that, at some scale (near Planck's scale), frontiers between the stones and the glue connecting the stones are no more so clearly defined.
The way we introduced the extended products is suggesting that topology is the common denominator. This is imposing the necessity to discover the criterium defining the proportion between stones and glue, not the proportion itself. Indeed, if we accept the existence and the reality of dark energy and if we relate it to the glue, then we allready know the proportion.
SBGB04v1.pdf [In English; 8 pages, protected; 0.897 MB; 10 July 2009].
Old investigations (etgb101.pdf) are reformulated and inserted into the very actual discussion concerning the Symmetry Breaking procedure.
The first goal is to connect the formalism of the weak hypercharge and of the weak isospin EM field strength tensor. I have the hope to achieve this step in making use of the "decompositions" of that tensor (see etgb100.pdf and later etgb100v3.pdf). Actually only a trivial scenario involving the Christoffel's cube with a trivial split of the extended product supposed to be involved into the discussion is examined. But one can easily develop scenarii with any cube and with non trivial splits. (This is an idea for the next coming sections).
A first generalization of the decompositions is proposed for SU(4).
- The problematic of "induced metrics" is analyzed more precisely. We get at least one family of Christoffel's cube which are solutions of the problem; provided the components of the potential EM field vector are linearly dependant. An extension of the discussion is started.
As exercise, we propose to built a standard model with SU(4). The reason for this is the existence of a llink with the exploration made a few years ago and consisting to write the Lorentz Einstein Law of motion under the formalism of a differentiel operator. One of the (matricial) coefficient of that operator can be interpreted as the allowed gauge transformation matrix.
June 2009
[in English; 5 pages; protected; 0.609 MB; 15 June 2009]. This section is the first one which is replacing my work inside a standardized approach. It is explaining why one can theoretically envisage situations for which a set of reduced Christoffel's cubes (interpreted as defining an extended product) are sufficient tools to define a familly of metrics within a conformal GTR approach. You need former sections of my work to accept the results contained here; please see etgb100.pdf (in English), etgbv2.pdf (in English) and Part 10 of chapter I (in french with English resumé). A scenario is proposed to mixt colors and flavors via the Christoffel's cubes. This work is actually more elaborate in a French document (in revision).
[In french; updated : 25 June; 8 pages; 0.995 MB] Important remark concerning the coincidence between different formalisms; solutions of the classical elastic string in a gravitation field, of the Goldstone Model and of the Ginzburg Landau Theory (supraconduction). And first considerations made to propose a new Lagrangien taking the work etgb100v3.pdf into account.
May 2009
Feynman04.pdf:
I begin a fundamental reflexion about "what is a particle". The Feynman approach is the guidind idea. In fact, since I could connect the classical equation of an elastic string with one of the solutions of the Einstein's fields equations applying in vacuo, I think that the influence of the fields of gravitation on the trajectories must be reconsidered and incorporated into the Feynman's integrals in another way as usualy done. This reflexion is also forcing us to think about the notion of spacetime volume again. A trivial argumentation demonstrates either that we cannot reduce the mathematical discussion to real numbers or that spacetime volumes cannot be calculated with the classical formula.
Conformalv2.pdf:
confronting the CFT and a personal approach including bilinearity and the possibility to project the Lorenz Einstein Law onto a flat Minkowskian world.
Feynman03.pdf:
short explanation (3 pages; free) about the way to connect the Klein Gordon equation and the Feynman propagators for (virtual) photons via the theory of extended products. I am in fact looking for coherence inside physics.
FB04.pdf:
The so-called geometric densities are explored.
FB03.pdf:
The Tartaglia Cardan method first proposes a new variable (the so-called Cardan variable). The former has been clearly connected to the 3D volumetric densities in FB02.pdf. This logical conclusion is now analyzed and connected to the work made in chapter I part 10. That means: even if I am not yet able to prove that my approach will give the masses of elementary particles, I am able to incorporate my approach inside a way of thinking based on the cubes defining extended products. The densities can be writen with the help of the components of these cubes.
April 2009
FB02.pdf:
This section defines the 3D volumetric densities of matter associated with the solutions of the polynôme of degree 3 resulting of our initial approach and obtained via the Tartaglia Cardan method.
FB01.pdf:
French explainations about the Baryons document.
Baryons [v1; 23/04/2009; 4 pages; adobe 9]
This is a very detailled analysis of the procedure exposed in Vacuum2.pdf: can we replace the relativistic volumic density of force by the one we have introduced a few years ago? In that sense, it is also an amelioration of the initial work of 2003.
The quest to discover the masses of elementary particles (here of baryons) is going further.
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Einstein's metrics are an essential ingredient to understand vacuum. I try to situate my work relatively to other approaches. I read new investigations made by the LQG "school" or by mathematicians. My "string theory" makes sense if it describes infinitesimal pieces of "dark energies" made strings. Do we have an example of what the Perimeter Institute calls "a disordered locality"?
Vacuumv2.pdf [v2 of the March version; 3 pages]
Going a step further. The way of thinking which is developped here is leading the discussion into the direction of the "Einstein's metrics". This is a very fascinating and complicated topic for an amateur like me. A lot of very interesting works have still been done. I actually need time to learn about that. Thanks for patience.
March 2009
Vacuum.pdf [31.03.2009; 2 pages; Adobe 9]
The document explains why one can make the choice to adopt a new formalism for the forces within a conform GTR approach. The new formalism implicitly corrresponds to a small set of plausible hypothese and has the same "beauty" than the formalism discovered for the partial derivate by respect for the time of the Poynting vector in Maxwell's vacuum.
The equivalence between both formalisms introduces two necessary relations. The analyze of which naturally yields a link with the gravitation and with an interpretation of particles as currents of presure or as infinitesimal dynamic strings.
But for a complete overview concerning the work made during March please visit the French presentation. I am rewriting old articless (2004) concerning a confrontation between a very classical model of elastic string and one possible solution of the generalized theory of relativity [GTR; volumetric density of energy + pressure = 0].
This gives me the oppotunity to explain my representation. The strict interpretation of the calculations indicates a possible correlation between the ability for the vaccum to be polarized (EM effects) and its ability to deform itself (gravitodynamics).
It is still known that deformations of the geometrical structure could give rise to particles. But former approaches in that direction (e.g. Birell... Quantum Field Theory in curved spacetime) are built on a specific way of thinking which is not directly involving mecanical considerations like I tried to do it.
The advantage of my quasi-empirical theoretical construction is the discovery of a direct link between elements imported from considerations about classical strings and a solution of the GTR.
The other important discovery, I think, is that the geometrical "elasticity" is the origin of polarizations. That means: deformations of the geometrical structure should "create" charges. A personal treatment of a demonstration due to Lamb and Rutherford at the quantum limit gives the explaination of the fundamental trinity encountered in vacuum: there certainly are trios of energetic states.
I don't have a definitive viewpoint but I am exploring this mysterious boarder between vacuo and elementary particles at Planck scale with a strong intellectual enthousiasm. My intuition is that there is a fundamental link between my string theory applied to the vacuum and the GLAC Theory (see vide05.pdf and the most recent investigation vide10.pdf - 28 March 2009).
This research is actual and represents a very modern approach to understand gravity, thus anti-gravity too.