Marc Henneaux - Böcker

This article is dedicated to Claudio Bunster on the occasion of his 60th birthday. It is a great honor to take this opportunity to express my gratitude to him, who in my opinion has been the greatest national physicist ever, for his wise guidance and intrepid support through the years. As a Chilean, I can further tell that Claudio’s contributions have been well far beyond theoretical physics, helping our country to be ready to face future challenges through science. Gravity in diverse dimensions is a subject in which Claudio has done major c- tributions, encouraging in many ways the following work, that is being made along different fronts in collaboration with my colleagues Diego Correa, Gustavo Dotti, Julio Oliva and David Tempo. Thepursuitforwormholesolutions,whicharehandlesinthespacetimetopology, it is as old as General Relativity and it has appeared in theoretical physics within different subjects, ranging from the attempt of describing physics as pure geometry, as in the Einstein–Rosen bridge model of a particle [1], to the concept of “charge withoutcharge”[2],aswell asindifferentissuesconcerningthe Euclideanapproach to quantum gravity (see, e.g., [3]). More recently, the systematic study of this kind of objects was pushed forward by the works of Morris, Thorne and Yurtsever [4,5].

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski-Khalatnikov-Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singularities, the billiard description, and emergent mathematical structures.

This article is dedicated to Claudio Bunster on the occasion of his 60th birthday. It is a great honor to take this opportunity to express my gratitude to him, who in my opinion has been the greatest national physicist ever, for his wise guidance and intrepid support through the years. As a Chilean, I can further tell that Claudio’s contributions have been well far beyond theoretical physics, helping our country to be ready to face future challenges through science. Gravity in diverse dimensions is a subject in which Claudio has done major c- tributions, encouraging in many ways the following work, that is being made along different fronts in collaboration with my colleagues Diego Correa, Gustavo Dotti, Julio Oliva and David Tempo. Thepursuitforwormholesolutions,whicharehandlesinthespacetimetopology, it is as old as General Relativity and it has appeared in theoretical physics within different subjects, ranging from the attempt of describing physics as pure geometry, as in the Einstein–Rosen bridge model of a particle [1], to the concept of “charge withoutcharge”[2],aswell asindifferentissuesconcerningthe Euclideanapproach to quantum gravity (see, e.g., [3]). More recently, the systematic study of this kind of objects was pushed forward by the works of Morris, Thorne and Yurtsever [4,5].

The almost irresistible beauty of string theory has seduced many theoretical physicists in recent years. Even hardened men have been swept away by what they can already see and by the promise of even more. It would appear fair to say that it is not yet clear what form the theory will finally take and in what precise way it will relate to the physical world. However, it would seem equally fair to state that, most likely, strings are here to stay and will playa profound and central role in our conception of the universe. There is therefore a pressing need to provide both practicing physicists and advanced students with ways to master quickly, but soundly, the basic principles of the theory. The present volume is a step in that direction. It contains a lucid presentation of the basic principles of string theory in forms which may survive future developments. The book is an outgrowth of lectures given by Lars Brink and Marc Henneaux at the Centro de Estudios Cientificos de Santiago. The lectures covered in a self-contained manner different but complementary aspects of the foundations of string theory.

This volume focuses on the recent developments of general relativity. On the theoretical side, the main issues addressed are the pressing questions of quantum gravity and related topics: supergravity, string theory, black hole physics, lower and higher dimensional models, geometry and topology. On the experimental side, recent progress in observational cosmology, in the study of structures in the universe and on the dark matter problem are reported.

Ever since 1911, the Solvay Conferences have shaped modern physics. The 23rd edition, chaired by 2004 Nobel Laureate David Gross, did not break with that tradition. It gathered most of the leading figures working on the central problem of reconciling Einstein's theory of gravity with quantum mechanics.These proceedings give a broad overview with unique insight into the most fundamental issues raised by this challenge for 21st century physics, by distinguished renowned scientists. The contributions cover: the status of quantum mechanics, spacetime singularities and breakdown of classical space and time, mathematical structures underlying the most promising attempts under current development, spacetime as an emergent concept, as well as cosmology and the cosmological constant puzzle. A historical overview of the Solvay conferences by historian of sciences Peter Galison opens the volume.In the Solvay tradition, the volume also includes the discussions among the participants — many of which were quite lively and illustrate dramatically divergent points of view — carefully edited and reproduced in full.

Ever since 1911, the Solvay Conferences have shaped modern physics. The 23rd edition, chaired by 2004 Nobel Laureate David Gross, did not break with that tradition. It gathered most of the leading figures working on the central problem of reconciling Einstein's theory of gravity with quantum mechanics.These proceedings give a broad overview with unique insight into the most fundamental issues raised by this challenge for 21st century physics, by distinguished renowned scientists. The contributions cover: the status of quantum mechanics, spacetime singularities and breakdown of classical space and time, mathematical structures underlying the most promising attempts under current development, spacetime as an emergent concept, as well as cosmology and the cosmological constant puzzle. A historical overview of the Solvay conferences by historian of sciences Peter Galison opens the volume.In the Solvay tradition, the volume also includes the discussions among the participants — many of which were quite lively and illustrate dramatically divergent points of view — carefully edited and reproduced in full.

Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics.All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics.

Ever since 1911, the Solvay Conferences have shaped modern physics. The 25th edition held in October 2011 in Brussels and chaired by David Gross continued this tradition and celebrated the first centennial of this illustrious series of conferences. The development and applications of quantum mechanics have always been the main threads in the history of the Solvay Conferences, hence the 25th Solvay conference gathered many of the leading figures working on a wide variety of profound problems in physics where quantum mechanical effects play a central role. The conference addressed some of the most pressing open questions in the field of physics.The proceedings contain the “rapporteur talks” which give a broad overview with unique insights by distinguished and renowned scientists. These lectures cover the seven sessions: “History and Reflections”, “Foundations of Quantum Mechanics and Quantum Computation”, “Control of Quantum Systems”, “Quantum Condensed Matter”, “Particles and Fields”, “Quantum Gravity and String Theory” and it ended with a general discussion attempting to arrive at a synthesis.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — some of which quite lively and involving dramatically divergent points of view — have been carefully edited and are reproduced in full.