scholarly journals Topology and chiral random matrix theory at nonzero imaginary chemical potential

2009 ◽  
Vol 79 (7) ◽  
Author(s):  
C. Lehner ◽  
M. Ohtani ◽  
J. J. M. Verbaarschot ◽  
T. Wettig
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Chemical Potential ◽  
Matrix Theory

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals Random matrix theory and quantum chromodynamics

2018 ◽  
Author(s):  
Gernot Akemann
Keyword(s):  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Space Time ◽  
Gaussian Unitary Ensemble ◽  
Density Correlation ◽  
Recent Developments ◽  
Matrix Problems

This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.

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