Fundamentals Of Many Body Physics

The goal of the present course on “Fundamentals of Theoretical Physics” is to be a direct accompaniment to the lower-division study of physics, and it aims at providing the ph- ical tools in the most straightforward and compact form as needed by the students in order to master theoretically more complex topics and problems in advanced studies and in research. The presentation is thus intentionally designed to be suf?ciently detailed and self-contained – sometimes, admittedly, at the cost of a certain elegance – to permit in- vidual study without reference to the secondary literature. This volume deals with the quantum theory of many-body systems. Building upon a basic knowledge of quantum mechanics and of statistical physics, modern techniques for the description of interacting many-particle systems are developed and applied to various real problems, mainly from the area of solid-state physics. A thorough revision should guarantee that the reader can access the relevant research literature without experiencing major problems in terms of the concepts and vocabulary, techniques and deductive methods found there. The world which surrounds us consists of very many particles interacting with one another, and their description requires in principle the solution of a corresponding number ofcoupledquantum-mechanicalequationsofmotion(Schrodinger ̈ equations),which,h- ever, is possible only in exceptional cases in a mathematically strict sense. The concepts of elementary quantum mechanics and quantum statistics are therefore not directly applicable in the form in which we have thus far encountered them. They require an extension and restructuring, which is termed “many-body theory”.

This textbook addresses the special physics of many-particle systems, especially those dominated by correlation effects. It develops modern methods to treat such systems and demonstrates their application through numerous appropriate exercises, mainly from the field of solid state physics. The book is written in a tutorial style appropriate for those who want to learn many-body theory and eventually to use this to do research work in this field. The exercises, together with full solutions for evaluating one's performance, help to deepen understanding of the main aspects of many-particle systems. This revised second edition presents new sections on the finite-temperature Matsubara formalism, in particular with respect to Dyson equation, the Hartree-Fock approximation, second order perturbation theory, spin density waves, Hubbard model, Jellium model, quasi particles, Fermi liquids and multi particle Matsubara functions. Completing the outstanding Theoretical Physics series, this book will be a valuable resource for advanced students and researchers alike.

The goal of the present course on “Fundamentals of Theoretical Physics” is to be a direct accompaniment to the lower-division study of physics, and it aims at providing the ph- ical tools in the most straightforward and compact form as needed by the students in order to master theoretically more complex topics and problems in advanced studies and in research. The presentation is thus intentionally designed to be suf?ciently detailed and self-contained – sometimes, admittedly, at the cost of a certain elegance – to permit in- vidual study without reference to the secondary literature. This volume deals with the quantum theory of many-body systems. Building upon a basic knowledge of quantum mechanics and of statistical physics, modern techniques for the description of interacting many-particle systems are developed and applied to various real problems, mainly from the area of solid-state physics. A thorough revision should guarantee that the reader can access the relevant research literature without experiencing major problems in terms of the concepts and vocabulary, techniques and deductive methods found there. The world which surrounds us consists of very many particles interacting with one another, and their description requires in principle the solution of a corresponding number ofcoupledquantum-mechanicalequationsofmotion(Schrodinger ̈ equations),which,h- ever, is possible only in exceptional cases in a mathematically strict sense. The concepts of elementary quantum mechanics and quantum statistics are therefore not directly applicable in the form in which we have thus far encountered them. They require an extension and restructuring, which is termed “many-body theory”.

This book explains the tools and concepts needed for a research-level understanding of the subject, for graduate students in condensed matter physics.

This textbook addresses the special physics of many-particle systems, especially those dominated by correlation effects. It develops modern methods to treat such systems and demonstrates their application through numerous appropriate exercises, mainly from the field of solid state physics. The book is written in a tutorial style appropriate for those who want to learn many-body theory and eventually to use this to do research work in this field. The exercises, together with full solutions for evaluating one's performance, help to deepen understanding of the main aspects of many-particle systems. This revised second edition presents new sections on the finite-temperature Matsubara formalism, in particular with respect to Dyson equation, the Hartree-Fock approximation, second order perturbation theory, spin density waves, Hubbard model, Jellium model, quasi particles, Fermi liquids and multi particle Matsubara functions. Completing the outstanding Theoretical Physics series, this book will be a valuable resource for advanced students and researchers alike.

Based on an established course and covering all the fundamentals, central areas and contemporary topics of this diverse field, Fundamentals of Condensed Matter Physics is a much-needed textbook for graduate students. Coverage of concepts and techniques ensures that both theoretically and experimentally inclined students gain the strong understanding needed for research and teaching.

The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.

The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.