2007/01/01 by K. Splittorff, J. J. M. Verbaarschot
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Chiral perturbation theory #Dirac operator #Discontinuity (linguistics) #Eigenvalues and eigenvectors #Lattice QCD #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Operator (biology) #Particle physics #Physics #QCD vacuum #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Random Matrices and Applications #Random matrix #Sign (mathematics) #Theoretical and Computational Physics #Theoretical physics #hep-ph
paper · pdf · doi:10.1143/ptps.168.265
published as Prog.Theor.Phys.Suppl.168:265-275,2007 · Invited talk at YKIS2006, YITP-Kyoto, 10 pages, 10 figures
openalex publication_date 2007/01/01 · arxiv created 2007/04/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We review applications of random matrix theory to QCD at nonzero temperature and chemical potential. The chiral phase transition of QCD and QCD-like theories is discussed in terms of eigenvalues of the Dirac operator. We show that for QCD at µ = 0, which has a sign problem, the discontinuity in the chiral condensate is due to an alternative to the Banks-Casher relation. The severity of the sign problem is analyzed in the microscopic domain of QCD. Starting from its introduction in nuclear physics by Wigner, 1) random matrix theories have been applied to a wide range of problems ranging from the physics of proteins 2) to quantum gravity (see 3),4) for a historical review). Three reasons for the ubiquity of random matrix theory come to mind. First, eigenvalues of large random