Date/heure
28 avril 2022
15:45 - 16:45
Oratrice ou orateur
Mohammed Takook (Kharazmi University, laboratoire "Astroparticules et Cosmologie”, CNRS & Université Paris Cité)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
The quantum gauge theory is the current basis for explaining the interactions of elementary particles. Among the four fundamental interactions: electromagnetic, weak, strong, and gravitational, for the last two, a proper mathematical construction does not yet exist. Quantum gauge theory is based on three different branches of mathematics: 1) geometry, 2) group theory, and 3) functional analysis.
The strong interactions are studied in the SU(3) quantum Yang-Mills theory but an axiomatic QFT with the mass gap and color confinement does not yet exist. In the classical field theory model, the gluon^1 is a massless particle but one can not see the color-charge^2 of a particle in nature, and then the gluons must be in the bound states, forming massive particles. This is the mass gap problem. The mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and the mass gap is the mass of the lightest particle. However, the color confinement postulated permits only bound states of gluons, it is an obvious contradiction.
In this presentation, I would like to discuss the fact that if we replace: 1) Minkowskian geometry with the de Sitterian geometry, 2) Poincaré group with de Sitter group and 3) Hilbert space quantization with the Krein space quantization, an axiomatic quantum Yang-Mills theory with a mass gap and the color confinement can be constructed. It is important to note that the ambient space formalism allows us to make this construction possible.
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1 . A gluon is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks.
2 . Color charge is a property of quarks and gluons that is related to the particles’ strong interactions in the theory of quantum chromodynamics