Synopses & Reviews
The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.
Synopsis
This book practical book applies integrable systems to solve the phase transition problems. It provides a unified model for the densities of eigenvalues in quantum chromodynamics (QCD).
About the Author
The author obtained his Ph.D in mathematics at University of Pittsburgh in 1998. Then he worked at University of California, Davis, as a visiting research assistant professor for one year before he started working in industry.
Table of Contents
Introduction.- Densities in Hermitian Matrix Models.- Bifurcation Transitions and Expansions.- Large-N Transitions and Critical Phenomena.- Densities in Unitary Matrix Models.- Transitions in the Unitary Matrix Models.- Marcenko-Pastur Distribution and McKay's Law.