Inherent holography in fuzzy spaces and an N-tropic approach to the cosmological constant problem

Sheikh-Jabbari, M. M.

doi:10.1016/j.physletb.2006.08.083

Cited by 15 publications

(19 citation statements)

References 25 publications

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“…This can be done on even-dimensional co-adjoint orbits of Lie groups, which are symplectic manifolds [43,44,45,46,47,48,49,50,51], like the two-sphere S 2 and the CP n complex projective spaces.…”

Section: Introductionmentioning

confidence: 99%

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Panero¹

2006

SIGMA

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Abstract. We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.

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Section: Introductionmentioning

confidence: 99%

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Panero¹

2006

SIGMA

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“…Since fuzzy spheres, are obtained from quantization of a compact space, they are described by finite dimensional matrices, in a way that the number of independent states defined on the fuzzy sphere is limited, and the entropy associated with these states is finite, in agreement with the Bekenstein's limit [28,34,[36][37][38][39].…”

Section: The Fuzzy Sphere Modelmentioning

confidence: 97%

“…Fuzzy spheres consist in one of the most simplest example of noncommutative spaces and appear as vacuum solutions in Euclidean gravity [33][34][35]. It is obtained when one quantizes the usual sphere S 2 replacing the commutative algebra of functions on this manifold by the noncommutative algebra of matrices.…”

Section: The Fuzzy Sphere Modelmentioning

confidence: 99%

Fuzzy Spheres Decays and Black Hole Thermodynamics

Silva¹

2012

Thermodynamics - Fundamentals and Its Application in Science

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However the understanding of black hole thermodynamics in the semiclassical and furthermore in quantum regime has been a very difficult, and still unsolved problem. To explain the situation, it is known that, in statistical physics, entropy counts the number of accessible microstates that a system can occupy, where all states are presumed to occur with equal externally observable classical parameters: mass, electric charge, and angular momentum. All other information about the matter which formed a black hole "disappears" behind its event horizon, and therefore the nature of these microstates is obscure. Thus, the origin of the black hole entropy is not clear. Furthermore, in order to justify the name "entropy", one must to explain also why the sum of the entropy of a black hole and the entropy of its vicinity is a non-decreasing function of time. In other words, why black holes obey the so called "Generalized Second Law of thermodynamics (GSL)".

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“…(98) bear an interesting statement of holography. In order to see the holography we argue in what follows that the smallest area that one can probe on S 2 F is given by [71] Area(min) = L min L max = L 2 P .…”

Section: The Ir/uv Mixing and "New" Cosmological Constant Problemmentioning

confidence: 99%

Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem

Jalalzadeh

Capistrano

Moniz

2017

Physics of the Dark Universe

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We endorse the context that the cosmological constant problem is a quantum cosmology issue. Therefore, in this paper we investigate the q-deformed Wheeler-DeWitt equation of a spatially closed homogeneous and isotropic Universe in the presence of a conformally coupled scalar field. Specifically, the quantum deformed Universe is a quantized minisuperspace model constructed from quantum Heisenberg-Weyl U q (h 4 ) and U q (su(1, 1)) groups. These intrinsic mathematical features allow to establish that (i) the scale factor, the scalar field and corresponding momenta are quantized and (ii) the phase space has a non-equidistance lattice structure. On the other hand, such quantum group structure provides us a new framework to discuss the cosmological constant problem. Subsequently, we show that a ultraviolet cutoff can be obtained at 10 −3 eV , i.e., at a scale much larger than the expected Planck scale. In addition, an infrared cutoff, at the size of the observed Universe, emerges from within such quantum deformation of Universe. In other words, the spectrum of the scale factor is upper bounded. Moreover, we show that the emerged cosmological horizon is a quantum sphere S 2 q or, alternatively, a fuzzy sphere S 2 F which explicitly exhibits features of the holographic principle. The corresponding number of fundamental cells equals the dimension of the Hilbert space and hence, the cosmological constant can be presented as a consequence of the quantum deformation of the FLRW minisuperspace.

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Inherent holography in fuzzy spaces and an N-tropic approach to the cosmological constant problem

Cited by 15 publications

References 25 publications

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Fuzzy Spheres Decays and Black Hole Thermodynamics

Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem

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