Exotic smoothness, noncommutative geometry, and particle physics
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We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is equipped with an exotic differential structure, a compact object of geometric origin may exist even if the spacetime is topologically trivial. Possible implications are discussed. AnSU(3) ⊗SU(2) ⊗U(1) gauge model is constructed. This model may not be realistic, but it shows what kind of physical phenomena might be expected due to the existence of exotic differential structures on the spacetime manifold.
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- Connes, A. (1983).Publications Mathematiques IHES,62, 44.Google Scholar
- Connes, A. (1990). inThe Interface of Mathematics and Physics, D. Quillen, G. Segal, and S. Tsou, eds., Clarendon Press, Oxford.Google Scholar
- Connes, A. (1994).Non-Commutative Geometry, Academic Press, New York.Google Scholar
- Garcia-Bondía, J. M. (n.d.). Preprint [hep-th/940475].Google Scholar
- Gilkey, P. B. (1984a).The Index Theorem and the Heat Equation, Princeton University Press, Princeton, New Jersey.Google Scholar
- Gilkey, P. B. (1984b).Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Publish or Perish, Wilmington, Delaware.Google Scholar
- Hurt, N. (1983).Geometric Quantization in Action, Reidel, Dordrecht.Google Scholar
- Kastler, D., and Schücker, T. (1992).Teoreticheskaya i Matematicheskaya Fizika,92, 223 [English translation,Theoretical and Mathematical Physics,1993, 1075].Google Scholar
- Sładkowski, J. (1996).Acta Physica Polonica B,27, 649.Google Scholar