Dirac Spectra in Dense QCD by Takuya Kanazawa

By Takuya Kanazawa

Gaining a theoretical figuring out of the homes of ultra-relativistic dense topic has been the most vital and tough pursuits in quantum chromodynamics (QCD). during this thesis, the writer analyzes dense quark topic in QCD with gauge team SU(2) utilizing low-energy powerful theoretical suggestions and elucidates a unique connection among statistical homes of the Dirac operator spectrum at excessive baryon chemical power and a different classification of random matrix theories. This paintings should be seen as an extension of an identical correspondence among QCD and matrix versions which was once formerly identified just for infinitesimal chemical potentials. In destiny numerical simulations of dense subject the analytical effects suggested listed below are anticipated to function a great tool to extract actual observables comparable to the BCS hole from numerical facts at the Dirac spectrum.

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ChRMT is a convenient mathematical tool to calculate statistical correlations of microscopic Dirac eigenvalues. 3. Analytical predictions from ChRMT are useful in extracting low energy constants from data obtained in lattice simulations which is inevitably done in a finite volume. Finally let us just outline how to compute the spectral correlation functions in ChRMT. At least three strategies are known: the method of (skew-)orthogonal polynomials, the replica trick and the supersymmetric method.

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