"why are nontrivial models of physical systems so often soluble in one dimension but not in three dimensions"

Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles (Perspectives in Physics : A Series of Reprint Collections)

Science & Math

Lieb, Elliott H.

Mattis, Daniel C.

Physics

Academic Pr

Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.

The Stability of Matter in Quantum Mechanics

Seiringer, Robert

Cambridge University Press

Description Not simply another book on real analysis, this straightforward, hands-on text provides readers at all levels--from beginning students to practicing analysts--with the basic concepts and standard tools necessary to understand analytical methods and better apply them to research in a variety of areas. 
Noted authorities Elliott Lieb and Michael Loss take readers quickly from basic topics to practical applications, incorporating only those results and constructions that work successfully in mathematics and its applications, while omitting typical textbook topics usually included for historical reasons or to achieve (sometimes unneeded) generality. Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to a new level of understanding with a minimum of fuss, while at the same time doing so in a rigorous and pedagogical way. 
The authors take great care to include topics that any working analyst uses in everyday practice. Unlike other books on the topic, Analysis does not try to laboriously develop subjects from basic principles to full generality. Instead, the book immediately starts working with a subject and shows its relation to other mathematical concepts, illustrating how the corresponding notions work, how to apply them in practice, and more. 
The book covers measure and integration, theory of $L^p$ spaces, distribution theory, Fourier analysis, potential theory, and Sobolev spaces. Certain less standard topics (such as rearrangement, integral, and Sobolev inequalities) are included to give the reader a flavor of research in analysis and to emphasize the open, active nature of this area. To illustrate the use of mathematics developed in the book, the concluding chapter contains three examples of solving problems from the calculus of variations. 
Analysis is a unique, practical book that everyone--from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods--will find interesting, stimulating, and useful.

Analysis (Graduate Studies in Mathematics, V. 14)

Loss, Michael

Mathematics

Amer Mathematical Society

Excellent current review of our knowledge of matter. In this new edition two new sections have been added: quantum electrodynamics and Boson systems.

The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. Lieb

History

Europe

Springer

This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.

Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb

This collection of papers -- starting with a brilliant article by one of the masters of the field -- gives an excellent current review of our knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text for a graduate course in quantum mechanics. In this new edition two new sections have been added: Section 7 contains papers on quantum electrodynamics, and Section 8 on Boson systems.

The Stability of Matter: From Atoms to Stars: Selecta of Elliot H. Lieb

Thirring, Walter E.

Astronomy & Space Science

Springer, Verlag

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Inequalities

The stability of matter: From atoms to stars : selecta of Elliott H. Lieb

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Inequalities: Selecta of Elliott H. Lieb

See the best price to sell, buy, or rent books by Lieb, Elliott H.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Lieb, Elliott H.

See the best price to sell, buy, or rent books by Lieb, Elliott H.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles (Perspectives in Physics : A Series of Reprint Collections)

The Stability of Matter in Quantum Mechanics

Analysis (Graduate Studies in Mathematics, V. 14)

The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. Lieb

Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb

The Stability of Matter: From Atoms to Stars: Selecta of Elliot H. Lieb

Inequalities

The stability of matter: From atoms to stars : selecta of Elliott H. Lieb

Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb

Inequalities: Selecta of Elliott H. Lieb