The Spectral Action for Dirac Operators with Skew-Symmetric Torsion

Communications in Mathematical Physics

Volumn 300, Issue 3, 2010, Pages 877-888

  Hanisch, Florian ^a   Pfäffle, Frank ^a   Stephan, Christoph A ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78149498458     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-010-1135-3     Document Type: Article

References (28)

1. Connes A.: Noncommutative Geometry. Academic Press, London-NewYork (1994).
2. Connes A.: Noncommutative geometry and reality. J. Math. Phys. 36, 6194 (1995).
3. Connes A.: Gravity coupled with matter and the foundation of noncommutative geometry. Commun. Math. Phys. 155, 109 (1996).
4. Connes, A., Marcolli, M.: Noncommutative Geometry, Quantum Fields and Motives. http://www. alainconnes. org/docs/bookwebfinal. pdf, 2007.
5. Chamseddine A., Connes A.: The spectral action principle. Commun. Math. Phys. 182, 155 (1996).
6. Chamseddine A., Connes A., Marcolli M.: Gravity and the standard model with neutrino mixing. Adv. Theor. Math. Phys. 11, 991 (2007).
7. Chamseddine A., Connes A.: Why the Standard Model. J. Geom. Phys. 58, 38 (2008).
8. Chamseddine A., Connes A.: Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model. Phys. Rev. Lett. 99, 191601 (2007).
9. Chamseddine A., Connes A.: Scale invariance in the spectral action. J. Math. Phys. 47, 063504 (2006).
10. Chamseddine A., Connes A.: Quantum Gravity Boundary Terms from Spectral Action. Phys. Rev. Lett. 99, 071302 (2007).
11. Agricola I., Friedrich T.: On the holonomy of connections with skew-symmetric torsion. Math. Ann. 328, 711 (2004).
12. Chamseddine, A., Connes, A.: Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I. http://arxiv. org/abs/1004. 0464v1 [hep-th], 2010.
13. Gilkey P. B.: Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (second edition). CRC Press, Boca Raton, FL (1995).
14. Nest R., Vogt E., Werner W.: Spectral Action and the Connes-Chamseddine Model. In: Scheck, F., Upmeier, H., Werner, W. (eds) Lecture Notes in Physics 596, pp. 109. Springer, Berlin-Heidelberg-NewYork (2002).
15. Goldthorpe W. H.: Spectral Geometry and SO(4) Gravity in a Riemann-Cartan Spacetime. Nucl. Phys. B170, 307 (1980).
16. Obukhov Yu. N.: Spectral Geometry Of The Riemann-Cartan Space-Time. Nucl. Phys. B212, 237 (1983).
17. Buchbinder I. L., Odintsov S. D., Shapiro I. L.: Nonsingular cosmological model with torsion induced by vacuum quantum effects. Phys. Lett. B162, 92 (1985).
18. Grensing G.: Induced Gravity For Nonzero Torsion. Phys. Lett. B169, 333 (1986).
19. Cognola G., Zerbini S.: Seeley-deWitt Coefficents in a Riemann-Cartan Manifold. Phys. Lett. B214, 70 (1988).
20. Salamon, S.: Riemannian geometry and holonomy groups. Pitman Research Notes in Mathematics Series 201; New York: Wiley & Sons, Inc., 1989.
21. Kalau W., Walze M.: Gravity, noncommutative geometry and the Wodzicki residue. J. Geom. Phys. 16, 327 (1995).
22. Ackermann, T., Tolksdorf, J.: The Generalized Lichnerowicz formula and analysis of Dirac operators. http://arxiv. org/abs/hep-th/9503153v1, 1995.
23. Iochum B., Kastler D., Schücker T.: On the universal Chamseddine-Connes action. I. Details of the action computation. J. Math. Phys. 38(10), 4929 (1997).
24. Perez A., Rovelli C.: Physical effects of the Immirzi parameter. Phys. Rev. D73, 044013 (2006).
25. Mercuri S.: Fermions in the Ashtekar-Barbero connection formalism for arbitrary values of the Immirzi parameter. Phys. Rev. D73, 084016 (2006).
26. Alexander, S., Vaid, D.: Gravity induced chiral condensate formation and the cosmological constant. http://arxiv. org/abs/hep-th/0609066v1, 2006;.
27. Alexander, S., Vaid, D.: A Fine tuning free resolution of the cosmological constant problem. http://arxiv. org/abs/hep-th/0702064v2, 2007;.
28. Alexander S., Biswas T.: Cosmological BCS mechanism and the Big Bang Singularity. Phys. Rev. D80, 023501 (2009).