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 play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H...
The mathematical study of the Bose gas goes back to the ?rst quarter of the twentieth century, with the invention of quantum mechanics. The name refers to the Indian physicist S.N. Bose who realized in 1924 that the statistics governing photons(essentiallyinventedbyMaxPlanckin1900)isdetermined(usingmodern terminology) by restricting the physical Hilbert space to be the symmetric tensor product of single photon states. Shortly afterwards, Einstein applied this idea to massive particles, such as a gas of atoms, and discovered the phenomenon that we now call Bose-Einstein condensation. At that...
The mathematical study of the Bose gas goes back to the ?rst quarter of the twentieth century, with the invention of quantum mechanics. The name refer...
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...
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, a...
In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a...
In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with rea...
This fourth edition of selecta of my work on the stability of matter contains recent work on two topics that continue to fascinate me: Quantum electrodynamics (QED) and the Bose gas. Three papers have been added to Part VII on QED. As I mentioned in the preface to the third edition, there must be a way to formulate a non-perturbative QED, presumably with an ultraviolet cutoff, that correctly describes low energy physics, i.e., ordinary matter and its interaction with the electromagnetic field. The new paper VII.5, which quantizes the results in V.9, shows that the elementary no-pair version...
This fourth edition of selecta of my work on the stability of matter contains recent work on two topics that continue to fascinate me: Quantum electro...
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...
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, a...
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 play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H...
Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the field. The contributions include both reviews and original results.
Contents: The Inverse r-Squared Force (Henry D. I. Abarbanel; Certain Hilbert Spaces of Analytic Functions Associated with the Heisenberg Group (Donald Babbitt); Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (John F. Barnes,...
Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contr...
