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- Three distinct geometries on S7 arise as solutions of the classical equations of motion in eleven dimensions. In addition to the conventional riemannian geometry, one can also obtain the two exceptional Cartan-Schouten compact flat geometries with torsion.
- The BEH mechanism operates within the context of gauge theories. Despite the fact that grand unification schemes reach scales comparable to the Planck scale, there was, a priori, no indication that Yang-Mills fields offer any insight into quantum gravity. The only approach to quantum gravity that had some success, in particular in the context of a quantum interpretation of the black hole entropies, are the superstring theory approaches and the possible merging of the five perturbative approaches (Type IIA, IIB, Type I and the two heterotic strings) into an elusive M-theory whose classical limit would be 11-dimensional supergravity.
- page 19 of (2002). "A brief course in spontaneous symmetry breaking ii. modern times: The BEH mechanism". arXiv preprint hep-th/0203097.
- What we hear about eternal inflation or the string landscape, seems somehow unavoidably to lead to some kind of multiverse. However, it seems to me there is a fundamental problem there. Once of course you have the multiverse, then you can start playing around and try to find probability or getting to the anthropic principle, or whatever. But the point is that the picture is essentially a classical one, and it is difficult to see that if you have many universes, coming essentially with an inflationary state, that there would not be plenty of horizons in this. Now the quantum mechanics of horizons is, I think, perfectly not understood. The simplest example is the black hole, where after all nobody knows really if the problem lies in the singularity or if it lies really already in the horizon.
- as quoted in: Gross, David; Henneaux, Marc; Sevrin, Alexander, eds. (2013). The Theory of the Quantum World: Proceedings of the 25th Solvay Conference on Physics, Brussels, Belgium 19-22 October 2011. World Scientific. p. 309.
- At the ULB, Brout and I initiated a research group in fundamental interactions, that is, in the search for the general laws of nature. Joined by brilliant students, many of them becoming world renowned physicists, our group contributed to the many fields at the frontier of the challenges facing contemporary physics. While the mechanism discovered in 1964 was developed all over the world to encode the nature of weak interactions in a "Standard Model," our group contributed to the understanding of strong interactions and quark confinement, general relativity and cosmology. There we introduced the idea of a primordial exponential expansion of the universe, later called inflation, which we related to the origin of the universe itself, a scenario, which I still think may possibly be conceptually the correct one. During these developments, our group extended our contacts with other Belgian universities and got involved in many international collaborations.
With our group and many other collaborators I analysed fractal structures, supergravity, string theory, infinite Kac-Moody algebras and more generally all tentative approaches to what I consider as the most important problem in fundamental interactions: the solution to the conflict between the classical Einsteinian theory of gravitation, namely general relativity, and the framework of our present understanding of the world, quantum theory.