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Book details
Author : Assa Auerbach
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Pages : 255 pages
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Publisher : Springer 1998-09-11
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Language : English
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ISBN-10 : 0387942866
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ISBN-13 : 9780387942865
Book Synopsis
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in
transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple)
logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some
was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years,
diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itinerÂ- ant
magnets, and superconductors. It is in essence a weak coupling expanÂ- sion about free quasiparticles. Many experimental discoveries
during the last decade, including heavy fermions, fractional quantum Hall effect, highÂ- temperature superconductivity, and quantum spin
chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of
alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly
interacting (or conÂ- strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for
fundamental concepts, such as effective HaÂ- miltonians, variational ground states, spontaneous symmetry breaking, and quantum
disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in
diverse areas of theoretical physics.