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Barrett, John W.; Glaser, Lisa (2015)
Publisher: IOP Publishing
Languages: English
Types: Article
Subjects: General Relativity and Quantum Cosmology, High Energy Physics - Lattice, High Energy Physics - Theory
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Some features are explained in terms of the theory of random matrices but other phenomena remain mysterious. Some of the models with a quartic action of symmetry-breaking type display a phase transition. Close to the phase transition the spectrum of a typical Dirac operator shows manifold-like behaviour for the eigenvalues below a cut-off scale.
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    • [1] J. Ambj rn, A. Goerlich, J. Jurkiewicz, and R. Loll. Nonperturbative Quantum Gravity. arXiv:1203.3591, March 2012.
    • [2] Jan Ambj rn, Berg nnur Durhuus, and Thordur Jonsson. Quantum Geometry. Cambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, UK, 2005.
    • [3] Takehiro Azuma, Subrata Bal, Keiichi Nagao, and Jun Nishimura. Nonperturbative studies of fuzzy spheres in a matrix model with the ChernSimons term. JHEP, 05:005, 2004.
    • [4] John W. Barrett. A Lorentzian version of the non-commutative geometry of the standard model of particle physics. J. Math. Phys., 48:012303, 2007.
    • [5] John W. Barrett. Matrix geometries and fuzzy spaces as nite spectral triples. J. Math. Phys., 56:082301, 2015.
    • [6] S. Chadha, G. Mahoux, and M. L. Mehta. A method of integration over matrix variables: II. Journal of Physics A: Mathematical and General, 14(3):579, March 1981.
    • [13] H. Grosse and P. Presnajder. The Dirac operator on the fuzzy sphere. Lett. Math. Phys., 33:171{182, 1995.
    • [14] Gael Guennebaud, Beno^t http://eigen.tuxfamily.org, 2010.
    • [15] Herbert W. Hamber. Quantum Gravity on the Lattice. Gen. Rel. Grav., 41:817{876, 2009.
    • [17] Joe Henson, David P. Rideout, Rafael D. Sorkin, and Sumati Surya. Onset of the Asymptotic Regime for Finite Orders. arXiv:1504.05902 [gr-qc], April 2015. arXiv: 1504.05902.
    • [18] Alexander Holfter and Mario Paschke. Moduli spaces of discrete gravity. 1. A Few points... J. Geom. Phys., 47:101, 2003.
    • [19] J. Madore. The Fuzzy sphere. Class. Quant. Grav., 9:69{88, 1992.
    • [20] M. L. Mehta and M. Gaudin. On the density of Eigenvalues of a random matrix. Nuclear Physics, 18:420{427, August 1960.
    • [21] Madan Lal Mehta. Random Matrices. Academic Press, October 2004.
    • [22] M. E. J. Newman and G. T. Barkema. Monte Carlo Methods in Statistical Physics. Clarendon Press, February 1999.
    • [23] Denjoe O'Connor, Brian P. Dolan, and Martin Vachovski. Critical Behaviour of the Fuzzy Sphere. JHEP, 12:085, 2013.
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