Vincent Rivasseau - Böcker

The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques.Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques.Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters:•  Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status•  Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background•  Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution•  Arnaud CASSAN, New Worlds Ahead: The Discovery of ExoplanetsReinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics “for the discovery of a supermassive compact object at the centre of our galaxy’”, alongside Roger Penrose “for the discovery that black hole formation is a robust prediction of the general theory of relativity”. The book corresponds to the twentieth Poincaré Seminar, held on November 21, 2015, at Institut Henri Poincaré in Paris.Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters:•  Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status•  Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background•  Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution•  Arnaud CASSAN, New Worlds Ahead: The Discovery of ExoplanetsReinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics “for the discovery of a supermassive compact object at the centre of our galaxy’”, alongside Roger Penrose “for the discovery that black hole formation is a robust prediction of the general theory of relativity”. The book corresponds to the twentieth Poincaré Seminar, held on November 21, 2015, at Institut Henri Poincaré in Paris.Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

This eighteenth volume in the Poincaré Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification.

This eighteenth volume in the Poincaré Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification.

The book contains articles from leading experts in different areas of biological physics. Topics ranging from cell dynamics to the evolution of multicellularity to conscious versus non-conscious evidence accumulation are reviewed and discussed, both from a theoretical and an experimental perspective. Furthermore, current developments of practical applications like magnetic tweezers for the study of DNA replication and brain imaging are presented.

This tenth volume in the Poincaré Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience.  Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

The book contains articles from leading experts in different areas of biological physics. Topics ranging from cell dynamics to the evolution of multicellularity to conscious versus non-conscious evidence accumulation are reviewed and discussed, both from a theoretical and an experimental perspective. Furthermore, current developments of practical applications like magnetic tweezers for the study of DNA replication and brain imaging are presented.

This tenth volume in the Poincaré Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience.  Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ζ-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ζ-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S.Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians.

This thirteenth volume of the Poincaré Seminar Series, Henri Poincaré, 1912-2012, is published on the occasion of the centennial of the death of Henri Poincaré in 1912. It presents a scholarly approach to Poincaré’s genius and creativity in mathematical physics and mathematics. Its five articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include “Poincaré’s Light” by Olivier Darrigol, a leading historian of science, who uses light as a guiding thread through much of Poincaré ’s physics and philosophy, from the application of his superior mathematical skills and the theory of diffraction to his subsequent reflections on the foundations of electromagnetism and the electrodynamics of moving bodies; the authoritative “Poincaré and the Three-Body Problem” by Alain Chenciner, who offers an exquisitely detailed, hundred-page perspective, peppered with vivid excerpts from citations, on the monumental work of Poincaré onthis subject, from the famous (King Oscar’s) 1889 memoir to the foundations of the modern theory of chaos in “Les méthodes nouvelles de la mécanique céleste.” A profoundly original and scholarly presentation of the work by Poincaré on probability theory is given by Laurent Mazliak in “Poincaré’s Odds,” from the incidental first appearance of the word “probability” in Poincaré’s famous 1890 theorem of recurrence for dynamical systems, to his later acceptance of the unavoidability of probability calculus in Science, as developed to a great extent by Emile Borel, Poincaré’s main direct disciple; the article by Francois Béguin, “Henri Poincaré and the Uniformization of Riemann Surfaces,” takes us on a fascinating journey through the six successive versions in twenty-six years of the celebrated uniformization theorem, which exemplifies the Master’s distinctive signature in the foundational fusion of mathematics and physics, on which conformal field theory, string theory and quantum gravityso much depend nowadays; the final chapter, “Harmony and Chaos, On the Figure of Henri Poincaré” by the filmmaker Philippe Worms, describes the homonymous poetical film in which eminent scientists, through mathematical scenes and physical experiments, display their emotional relationship to the often elusive scientific truth and universal “harmony and chaos” in Poincaré’s legacy.This book will be of broad general interest to physicists, mathematicians, philosophers of science and historians.

The International Conference on Theoretical Physics, TH-2002, took place in Paris from July 22 to 27 in the Conference Center of the UNESCO, the United Nations Educational Scientific and Cultural Organization, under aegis of the IUPAP, the International Union of Pure and Applied Physics and of the French and Euro­ pean Physical Societies, with a large support of several French, European and international Institutions. International and crossdisciplinary, TH-2002 welcomed around 1200 partic­ ipants representing all domains of modern theoretical physics. The conference offered a high-level scientific program, including 18 plenary lectures, 45 general lectures in thematic sessions and 140 more specialized lectures, partly invited and partly selected among proposals received from participants. Around 500 contribu­ tions were also presented as posters. Plenary lectures as well as general thematic lectures were addressed to a general audience of theoricians, not only to specialists. According to our commitments towards UNESCO and other sponsoring insti­ tutions, TH-2002 attributed more than 200 fellowships, mostly to scientists from developing countries and Eastern Europe, covering registration fees and, for more than half of them, stay expenses with student type accomodation. Special highlights of the conference included • the opening ceremony on July 22, with the participation of Mrs Claudie Haignere, French Minister of Research, and M. Walter Erdelen, General Ad­ joint Director for Sciences at UNESCO. Their opening addresses were espe­ cially appreciated and are reproduced below. This ceremony preceded the first lecture by Professor Cohen-Tannoudji, Physics Nobel prize winner.

This fourteenth volume in the Poincaré Seminar Series is devoted to Niels Bohr, his foundational contributions to understanding atomic structure and quantum theory and their continuing importance today. - Serge Haroche & Jean-Michel Raimond, Bohr's Legacy in Cavity QED;

This fourteenth volume in the Poincaré Seminar Series is devoted to Niels Bohr, his foundational contributions to understanding atomic structure and quantum theory and their continuing importance today. - Serge Haroche & Jean-Michel Raimond, Bohr's Legacy in Cavity QED;

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M.

This volume provides a detailed description of the seminal theoretical construction in 1964, independently by Robert Brout and Francois Englert, and by Peter W. Higgs, of a mechanism for short-range fundamental interactions, now called the Brout-Englert-Higgs (BEH) mechanism. It accounts for the non-zero mass of elementary particles and predicts the existence of a new particle - an elementary massive scalar boson. In addition to this the book describes the experimental discovery of this fundamental missing element in the Standard Model of particle physics. The H Boson, also called the Higgs Boson, was produced and detected in the Large Hadron Collider (LHC) of CERN near Geneva by two large experimental collaborations, ATLAS and CMS, which announced its discovery on the 4th of July 2012.This new volume of the Poincaré Seminar Series, The H Boson, corresponds to the nineteenth seminar, held on November 29, 2014, at Institut Henri Poincaré in Paris.

The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

Addressing graduate students and researchers in physics and mathematics, this book fills a gap in the literature. It is an introduction into modern constructive physics, field theory and statistical mechanics and a survey on the most recent research in this field. It presents the main technical tools such as cluster expansion and their implementation in the rigorous renormalization group, and studies physical models in some detail. The reader will find a study of the ultraviolet limit of the Gross-Neveu model, of continuous symmetry breaking and of self-avoiding random walks in statistical mechanics, as well as applications to solid-state physics. Mathematicians will find constructive methods useful for studies in partial differential equations.

The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.

The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.

Theoretical physics is a vast set of subjects, ideas and methods, with wide and unexpected applications to many interdisciplinary problems. But no general international conference had tried to review in depth this huge and burgeoning field since the Trieste conference in 1968. The International Conference on Theoretical Physics, TH-2002, which took place at the Unesco building, Paris, from July 22 to 27, 2002, addressed this challenge.The reader will find in this book all invited and received contributions to the conference. After the general lectures of Nobel prize winners Anderson and Yang, the contributions by experts cover all aspects of modern theoretical physics ranging from particle physics, string theory, cosmology, statistical and condensed matter physics to dynamical systems and quantum chaos, the physics/biology interface, information theory and quantum computing.

The Poincare Seminar is held twice a year at the Institute Henri Poincare in Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation.This volume contains the lectures of the third and fourth Poincare Seminar, both held in 2003. The third one is devoted to Bose-Einstein Condensation: it covers the physics of superfluid liquid helium as well as the recently discovered atomic Bose-Einstein condensates. Major experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth one concentrates on Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and including theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium.Contributing authors:Roger BalianSebasten BalibarClaude Cohen-TannoudjiJean DalibardThibault DamourOlivier DarrigolChristian MaesPhilippe NozieresFelix RitortChristophe SalomonGora V.Shlyapnikov

This volume contains the third and fourth Poincaré Seminar, both held in 2003. The third one is devoted to Bose-Einstein Condensation: it covers the physics of superfluid liquid helium as well as the recently discovered atomic Bose-Einstein condensates. Major experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth one is devoted to Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and includes theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium.

This book is the third in a series of lectures of the S' eminaire Poincar' e,whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up to date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphi", this Poincar' e Seminar is held twice a year at the Institut Henri Poincar' ein Paris,with contri- tions prepared in advance. A particular care is devoted to the pedagogical nature of the presentation so as to ful?ll the goal of being readable by a large audience of scientists. ThisvolumecontainsthesixthsuchSeminar,heldin2004.Itisdevotedtothe Quantum Hall E?ect. After a historical and general presentation by Nobel prize Klaus von Klitzing, discoverer of this e?ect, the volume proceeds with reviews on the mathematics and physics of both the integer and fractional case, and includes up to date presentations of the tunneling and metrology experiments related to the Quantum Hall E?ect.We hopethat the publicationof this serieswill servethe community of phy- cists and mathematicians at professional or graduate student level. ' We thank the Commissariat 'al'Energie Atomique (Division des Sciences de laMati' ere),theCentreNationaldelaRechercheScienti?que(SciencesPhysiqueet Math' ematiques), and the Daniel Iagolnitzer Foundation for sponsoring the Se- nar. Special thanks are due to Chantal Delongeas for the preparation of the m- uscript.

This book is the fourth in a series of lectures of the S´ eminaire Poincar´ e,whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed “Bourbaphi”, the Poincar´ e Seminar is held twice a year at the Institut Henri Poincar´ e in Paris, with cont- butions prepared in advance. Particular care is devoted to the pedagogical nature of the presentations so as to ful?ll the goal of being readable by a large audience of scientists. This volume contains the seventh such Seminar, held in 2005. It is devoted to Einstein’s 1905 papers and their legacy. After a presentation of Einstein’s ep- temological approach to physics, and the genesis of special relativity, a cen- nary perspective is o?ered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein’s light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion. We hopethatthe publicationofthis serieswill servethe community ofphy- cists and mathematicians at the graduate student or professional level.

This volume is devoted to Quantum Decoherence with lectures from the Seminaire Poincare, held in November 2005 at the Institute Henri Poincare Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation.