Synopses & Reviews
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 own 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. Here 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 or recommended reading for a graduate course in quantum mechanics. In the third edition, two new sections were added: one contains papers on quantum electrodynamics, and the other on Boson systems. In this fourth edition, these topics have been further developed, extending the book by approximately 120 pages.
Review
From the reviews: "The rapid soldout of the two previous editions by itself demonstrates the high value of this book. The reader will have indeed the opportunity to gaze on the formidable mastering of functional analysis by Elliot Lieb and to discover mathematical and Physical depths in the description of, after all, familar physical phenomena. [...] The third edition contains new developments compared to previous ones, witnessing that the field is still lively. In particular there are important results concerning systems of bosons. [...] In conclusion, this book is a delight for readers interested in the stability and related properties of many-body systems. It, moreover, offers the oppertunity to admire the elegant mathematical considerations and the penetrating physical insight of a great theoretician." (Physicalia, 2002)
Review
From the reviews:
"The rapid soldout of the two previous editions by itself demonstrates the high value of this book. The reader will have indeed the opportunity to gaze on the formidable mastering of functional analysis by Elliot Lieb and to discover mathematical and Physical depths in the description of, after all, familar physical phenomena. [...] The third edition contains new developments compared to previous ones, witnessing that the field is still lively. In particular there are important results concerning systems of bosons. [...] In conclusion, this book is a delight for readers interested in the stability and related properties of many-body systems. It, moreover, offers the oppertunity to admire the elegant mathematical considerations and the penetrating physical insight of a great theoretician." (Physicalia, 2002)
Synopsis
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 of relativistic QED (using the Dirac operator) is unstable when many-body effects are taken into account. Stability can be restored, however, if the Dirac operator with the field, instead of the bare Dirac operator, is used to define an electron. Thus, the notion of a bare electron without its self-field is physically questionable."
Synopsis
Excellent current review of our knowledge of matter. In this new edition two new sections have been added: quantum electrodynamics and Boson systems.