This chapter provides an introduction to Green's functions in condensed matter physics. This is presented in a rather formal way, but this is necessary in order to do anything further with the functions. This technique allows the interacting system to be treated as 'solid' within well-characterizable approximations, still widely used today, but also provides the language used in modern computer-based simulations as well as for the interpretation of experiments.
This chapter provides an introduction to Green's functions in condensed matter physics. This is presented in a rather formal way, but this is necessary in order to do anything further with the functions. This technique allows the interacting system to be treated as 'solid' within well-characterizable approximations, still widely used today, but also provides the language used in modern computer-based simulations as well as for the interpretation of experiments.
This book will introduce advanced concepts and topics of solid-state theory. To this end we need a tool box that enables us to treat electron–electron interactions, and possibly also electron–phonon or phonon–phonon interactions in some well-defined, approximate way. The most advanced, yet still feasible approach, is the Green's function technique and the perturbation expansion using Feynman diagrams. This technique allows the interacting system to be treated as 'solid' within well-characterizable approximations, still widely used today, but also provides the language used in modern computer-based simulations as well as for the interpretation of experiments.
The chapter begins with a brief survey of concepts and techniques of experimental condensed matter physics. It will be shown how correlation functions provide a bridge between concrete experimental data and the theoretical formalism developed in previous chapters. Specifically we discuss – an example of outstanding practical importance – how the response of many-body systems to various types of electromagnetic perturbation can be described in terms of correlation functions and how these functions can be computed by field theoretical means. In the previous chapters we have introduced important elements of the theory of quantum many-body systems. Perhaps most importantly, we have learned how to map the basic microscopic representations of many-body systems onto effective low-energy models. However, to actually test the power of these theories, we need to understand how they can be related to experiment. This will be the principal subject of the present chapter. Modern condensed matter physics benefits from a plethora of sophisticated and highly refined techniques of experimental analysis including the following: electric and thermal transport; neutron, electron, Raman, and X-ray scattering; calorimetric measurements; induction experiments; and many more (for a short glossary of prominent experimental techniques, see Section 7.1.2 below). While a comprehensive discussion of modern experimental condensed matter would reach well beyond the scope of the present text, it is certainly profitable to attempt an identification of some structures common to most experimental work in many-body physics.
The chapter begins with a brief survey of concepts and techniques of experimental condensed matter physics. It will be shown how correlation functions provide a bridge between concrete experimental data and the theoretical formalism developed in previous chapters. Specifically we will discuss – an example of outstanding practical importance – how the response of many-body systems to various types of electromagnetic perturbations can be described in terms of correlation functions and how these functions can be computed by field theoretical means. In the previous chapters we have introduced important elements of the theory of quantum many-body systems. Perhaps most importantly, we have learned how to map the basic microscopic representations of many-body systems onto effective low-energy models. However, to actually test the power of these theories, we need to understand how they can be related to experiment. This will be the principal subject of the present chapter. Modern condensed matter physics benefits from a plethora of sophisticated and highly refined techniques of experimental analysis including the following: electric and thermal transport; neutron, electron, Raman, and X-ray scattering; calorimetric measurements; induction experiments; and many more (for a short glossary of prominent experimental techniques, see Section 7.1.2 below). While a comprehensive discussion of modern experimental condensed matter would reach well beyond the scope of the present text, it is certainly profitable to attempt an identification of some structures common to most experimental work in many-body physics.
A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and offers a review of the essential elements of quantum mechanics, solid state physics and statistical mechanics. Alongside a detailed account of the method of second quantization, the book covers topics such as Green's and correlation functions, diagrammatic techniques and superconductivity, and contains several case studies. Some background knowledge in quantum mechanics, solid state physics and mathematical methods of physics is assumed. Detailed derivations of formulas and in-depth examples and chapter exercises from various areas of condensed matter physics make this a valuable resource for both researchers and advanced undergraduate students in condensed matter theory, many-body physics and electrical engineering. Solutions to exercises are available online.
A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many-body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.
The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.