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Dirac Operators and Clifford Geometry — New Unifying Principles in Particle Physics?

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Clifford Algebras and Their Application in Mathematical Physics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 94))

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Abstract

In this lecture I will report on some recent progress in understanding the relation of Dirac operators on Clifford modules over an even-dimensional closed Riemannian manifold M and (euclidean) Einstein-Yang-Mills-Higgs models.

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References

  1. Ackermann T. A Note on the Wodzicki Residue, to appear in Journ. of Geom. and Physics.

    Google Scholar 

  2. Ackermann T. Supersymmetry and the generalized Lichnerowicz formula, dg-ga/9601004.

    Google Scholar 

  3. Ackermann T. Dirac Operators and Particle Models, Part I: Yang-Mills-Higgs coupled to Gravity, to appear.

    Google Scholar 

  4. Ackermann T. Dirac Operators and Particle Models, Part II, forthcoming.

    Google Scholar 

  5. Ackermann T. and Tolksdorf J. (1996) The generalized Lichnerowicz formula and analysis of Dirac operators, Journ. reine angew. Math. 471, 23–42.

    MathSciNet  MATH  Google Scholar 

  6. Ackermann T. and Tolksdorf J. A Unification of Gravity and Yang-Mills-Higgs Gauge Theories, CPT-95/P.3180.

    Google Scholar 

  7. Berline N., Getzler E. and Vergne M. (1992) Heat kernels and Dirac operators, Springer.

    Google Scholar 

  8. Connes A. Gravity coupled with matter and the foundation of non commutative geometry, hep-th/9603053.

    Google Scholar 

  9. Damour T. (1995) General Relativity and Experiment, Proc. of the XI th International Congress of Math. Physics, Editor D. Iagolnitzer, Intern. Press.

    Google Scholar 

  10. Iochum B. and Schücker T. (1996) Yang-Mills-Higgs versus Connes-Lott, Com. Math. Phys. 178, 1–26.

    Article  MATH  Google Scholar 

  11. Nachtmann O. (1986) Elementarteilchenphysik, Phänomene und Konzepte, Vieweg.

    Google Scholar 

  12. Ne’eman Y. and Sternberg S. (1991) Internal Supersymmetry and Superconnections, Sympl. Geom. and Math. Physics, Birkhäuser.

    Google Scholar 

  13. Quillen D. (1985) Superconnections and the Chern Character, Toplology 24, 89–95.

    MathSciNet  MATH  Google Scholar 

  14. Wodzicki M. (1987) Non-commutative residue I, LNM 1289, 320–399.

    MathSciNet  Google Scholar 

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Ackermann, T. (1998). Dirac Operators and Clifford Geometry — New Unifying Principles in Particle Physics?. In: Dietrich, V., Habetha, K., Jank, G. (eds) Clifford Algebras and Their Application in Mathematical Physics. Fundamental Theories of Physics, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5036-1_1

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  • DOI: https://doi.org/10.1007/978-94-011-5036-1_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6114-8

  • Online ISBN: 978-94-011-5036-1

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