Physics and Mathematics of Quantum Many-Body Systems

藤 陽平

Detlef Lehmann

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and when they break down. At the same time, its clear explanations and methodical, step-by-step calculations shed welcome light on the established physics literature.

Alexandre M. Zagoskin

Alexandre M. Zagoskin

Emanuela L. Giacomelli, Jinyeop Lee, Marius Lemm

The mathematical study of quantum many-body physics has seen significant breakthroughs in the past 15–20 years. Mathematical physicists have approached these systems from different perspectives with different methods. The mini-workshop aimed to connect two rapidly growing fields: the mathematical analysis of many-body systems in scaling regimes (which has led to precise asymptotic formulas of the ground state energy and time evolution, e.g., of Bose gases) and the study of strongly correlated quantum systems via Lieb-Robinson bounds (which provide fundamental insights into the spreading of quantum information).

The mathematical study of quantum many-body physics has seen significant breakthroughs in the past 15–20 years. Mathematical physicists have approached these systems from different perspectives with different methods. The mini-workshop aimed to connect two rapidly growing fields: the mathematical analysis of many-body systems in scaling regimes (which has led to precise asymptotic formulas of the ground state energy and time evolution, e.g., of Bose gases) and the study of strongly correlated quantum systems via Lieb-Robinson bounds (which provide fundamental insights into the spreading of quantum information).