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Register a new userHiggs Boson Mass predicted by the Four Color Theorem
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Added by
Vladimir Khachatryan
Publication date
2009
fields
Physics
and research's language is
English
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We show that the mathematical proof of the four color theorem yields a perfect interpretation of the Standard Model of particle physics. The steps of the proof enable us to construct the t-Riemann surface and particle frame which forms the gauge. We specify well-defined rules to match the Standard Model in a one-to-one correspondence with the topological and algebraic structure of the particle frame. This correspondence is exact - it only allows the particles and force fields to have the observable properties of the Standard Model, giving us a Grand Unified Theory. In this paper, we concentrate on explicitly specifying the quarks, gauge vector bosons, the Standard Model scalar Higgs $H^{0}$ boson and the weak force field. Using all the specifications of our mathematical model, we show how to calculate the values of the Weinberg and Cabibbo angles on the particle frame. Finally, we present our prediction of the Higgs $H^{0}$ boson mass $M_{H^{0}} = 125.992 simeq 126 GeV$, as a direct consequence of the proof of the four color theorem.
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In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have verified those statements using a computer. Here we give additional details for one of those lemmas, and we include the original computer programs and data as ancillary files accompanying this submission.
The usual Chern-Simons extension of Einstein gravity theory consists in adding a squared Riemann contribution to the Hilbert Lagrangian, which means that a square-curvature term is added to the linear-curvature leading term governing the dynamics of the gravitational field. However, in such a way the Lagrangian consists of two terms with a different number of curvatures, and therefore not homogeneous. To develop a homogeneous Chern-Simons correction to Einstein gravity we may, on the one hand, use the above-mentioned square-curvature contribution as the correction for the most general square-curvature Lagrangian, or on the other hand, find some linear-curvature correction to the Hilbert Lagrangian. In the first case, we will present the most general square-curvature leading term, which is in fact the already-known re-normalizable Stelle Lagrangian. In the second case, the topological current has to be an axial-vector built only in terms of gravitational degrees of freedom and with a unitary mass dimension, and we will display such an object. The comparison of the two theories will eventually be commented.
In this paper, we apply an equivalent color transform (ECT) for a minimal $k$-coloring of any graph $G$. It contracts each color class of the graph to a single vertex and produces a complete graph $K_k$ for $G$ by removing redundant edges between any two vertices. Based on ECT, a simple proof for four color theorem for planar graph is then proposed.
We report on the calculation of virtual processes contributing to the production of a Higgs boson and two jets in hadron-hadron collisions. The coupling of the Higgs boson to gluons, via a virtual loop of top quarks, is treated using an effective theory, valid in the large top quark mass limit. The calculation is performed by evaluating one-loop diagrams in the effective theory. The primary method of calculation is a numerical evaluation of the virtual amplitudes as a Laurent series in $D-4$, where $D$ is the dimensionality of space-time. For the cases $H to qbar{q}qbar{q}$ and $H to qbar{q}qbar{q}$ we confirm the numerical results by an explicit analytic calculation.
For the four-color theorem that has been developed over one and half centuries, all people believe it right but without complete proof convincing all1-3. Former proofs are to find the basic four-colorable patterns on a planar graph to reduce a map coloring4-6, but the unavoidable set is almost limitless and required recoloring hardly implements by hand7-14. Another idea belongs to formal proof limited to logical operation15. However, recoloring or formal proof way may block people from discovering the inherent essence of a coloring graph. Defining creation and annihilation operations, we show that four colors are sufficient to color a map and how to color it. We find what trapped vertices and boundary-vertices are, and how they decide how many colors to be required in coloring arbitrary maps. We reveal that there is the fourth color for new adding vertex differing from any three coloring vertices in creation operation. To implement a coloring map, we also demonstrate how to color an arbitrary map by iteratively using creation and annihilation operations. We hope our hand proof is beneficial to understand the mechanisms of the four-color theorem.
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