Annotations to Quantum Statistical Mechanics

This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He started the tedious work of rewriting and annotating them to fully understand the formalism of nonequilibrium quantum statistical mechanics. While doing so, he realized they can be a useful resource for students of modern physics but will have to be upgraded to match pace with the evolved curricula. Being aware that besides completing the course work and passing the relevant examinations, it is necessary for graduate students of modern physics to make the knowledge of a topic concrete in their minds. This book is a systematically prepared summary of those lectures and will be extremely useful for graduate students as well as senior researchers to settle down the key knowledge of the subject.

1. Physical Prerequisites 2. Mathematical Introduction 3. Information Contained in G> and G< 4. The Hartree and Hartree-Fock Approximations 5. Effects of Collisions on G 6. A Technique for Deriving Green’s Function Approximations 7. Transport Phenomena 8. Hartree Approximation, Collision-Less Boltzmann Equation, and Random Phase Approximation 9. Relation Between Real and Imaginary Time Response Functions 10. Slowly Varying Disturbances and the Boltzmann Equation 11. Quasi-Equilibrium Behavior: Sound Propagation 12. The Landau Theory of the Normal Fermi Liquid 13. Shielded Potential 14. T Approximation

In-Gee Kim is president of KimCNets, South Korea. He earned his PhD from Inha University, South Korea, in 2003, after which he worked with POSTECH, South Korea, as a post-doctoral researcher till 2005 and as an associate research professor till 2014. He was also with Northwestern University, Evanston, USA, as a post-doctoral research associate from 2004 to 2006. He moved to New Mexico Consortium, Inc., USA, in 2014 as associate research scientist and then to Lab021, LLC., South Korea, in 2016 as principal scientist. He was a research professor in Yonsei University, South Korea, till 2017.