Fuzzy Field Theory as a Random Matrix Model
Item
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Title
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Fuzzy Field Theory as a Random Matrix Model
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Identifier
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d_2009_2013:dad73731758e:11856
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identifier
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12477
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Creator
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Tekel, Juraj,
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Contributor
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V. Parameswaran Nair
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Date
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2013
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Language
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English
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Publisher
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City University of New York.
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Subject
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Theoretical physics | fuzzy field theory | matrix models
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Abstract
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This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices.;First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables.;We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case.;Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Physics
