Lectures on the Infrared Structure of Gravity and Gauge Theory

Lectures on the Infrared Structure of Gravity and Gauge Theory

Author: Andrew Strominger

Publisher: Princeton University Press

Published: 2018-03-06

Total Pages: 198

ISBN-13: 0691179735

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A short, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the field Lectures on the Infrared Structure of Gravity and Gauge Theory presents an accessible, graduate-level synthesis of a frontier research area in theoretical physics. Based on a popular Harvard University course taught by the author, this book gives a concise introduction to recent discoveries concerning the structure of gravity and gauge theory at very long distances. These discoveries unite three disparate but well-developed subjects in physics. The first subject is the soft theorems, which were found by particle physicists in the 1950s to control the behavior of low-energy photons and are essential for all collider predictions. The second subject is asymptotic symmetries, found by general relativists in the 1960s to provide a surprising, infinite number of exact relations between distinct physical phenomena. The third subject is the memory effect, the measurement of which is sought in upcoming gravitational wave observations. An exploration of the physical and mathematical equivalence of these three subjects has provided a powerful new perspective on old results and led to a plethora of new results, involving symmetries of QED, gluon scattering amplitudes, flat-space holography in quantum gravity, black hole information, and beyond. Uniquely connective and cutting-edge, Lectures on the Infrared Structure of Gravity and Gauge Theory takes students and scholars to the forefront of new developments in the discipline. Materials are presented in a "lecture notes" style with problem sets included Concise and accessible pedagogical approach Topics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes


Book Synopsis Lectures on the Infrared Structure of Gravity and Gauge Theory by : Andrew Strominger

Download or read book Lectures on the Infrared Structure of Gravity and Gauge Theory written by Andrew Strominger and published by Princeton University Press. This book was released on 2018-03-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the field Lectures on the Infrared Structure of Gravity and Gauge Theory presents an accessible, graduate-level synthesis of a frontier research area in theoretical physics. Based on a popular Harvard University course taught by the author, this book gives a concise introduction to recent discoveries concerning the structure of gravity and gauge theory at very long distances. These discoveries unite three disparate but well-developed subjects in physics. The first subject is the soft theorems, which were found by particle physicists in the 1950s to control the behavior of low-energy photons and are essential for all collider predictions. The second subject is asymptotic symmetries, found by general relativists in the 1960s to provide a surprising, infinite number of exact relations between distinct physical phenomena. The third subject is the memory effect, the measurement of which is sought in upcoming gravitational wave observations. An exploration of the physical and mathematical equivalence of these three subjects has provided a powerful new perspective on old results and led to a plethora of new results, involving symmetries of QED, gluon scattering amplitudes, flat-space holography in quantum gravity, black hole information, and beyond. Uniquely connective and cutting-edge, Lectures on the Infrared Structure of Gravity and Gauge Theory takes students and scholars to the forefront of new developments in the discipline. Materials are presented in a "lecture notes" style with problem sets included Concise and accessible pedagogical approach Topics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes


Higher Spin Gauge Theories

Higher Spin Gauge Theories

Author: Nicolas Boulanger

Publisher: MDPI

Published: 2018-08-09

Total Pages: 459

ISBN-13: 303842997X

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This book is a printed edition of the Special Issue "Higher Spin Gauge Theories" that was published in Universe


Book Synopsis Higher Spin Gauge Theories by : Nicolas Boulanger

Download or read book Higher Spin Gauge Theories written by Nicolas Boulanger and published by MDPI. This book was released on 2018-08-09 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Higher Spin Gauge Theories" that was published in Universe


Towards Infrared Finite S-matrix in Quantum Field Theory

Towards Infrared Finite S-matrix in Quantum Field Theory

Author: Hayato Hirai

Publisher: Springer Nature

Published: 2021-07-17

Total Pages: 134

ISBN-13: 9811630453

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This book presents the better understanding of infrared structures of particle scattering processes in quantum electrodynamics (QED) in four-dimensional spacetime. An S-matrix is the fundamental quantity in scattering theory. However, if a theory involves massless particles, such as QED and gravity, the conventional S-matrix has not been well defined due to the infrared divergence, and infrared dynamics thus needs to be understood in-depth to figure out the S-matrix. The book begins with introducing fundamental nature of the charge conservation law associated with asymptotic symmetry, and explaining its relations to soft theorems and memory effect. Subsequently it looks into an appropriate asymptotic state of the S-matrix without infrared divergences. The Faddeev-Kulish dressed state is known as a candidate of such a state, and its gauge invariant condition and its relation to the asymptotic symmetry are discussed. It offers an important building blocks for constructing the S-matrix without infrared divergences.


Book Synopsis Towards Infrared Finite S-matrix in Quantum Field Theory by : Hayato Hirai

Download or read book Towards Infrared Finite S-matrix in Quantum Field Theory written by Hayato Hirai and published by Springer Nature. This book was released on 2021-07-17 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the better understanding of infrared structures of particle scattering processes in quantum electrodynamics (QED) in four-dimensional spacetime. An S-matrix is the fundamental quantity in scattering theory. However, if a theory involves massless particles, such as QED and gravity, the conventional S-matrix has not been well defined due to the infrared divergence, and infrared dynamics thus needs to be understood in-depth to figure out the S-matrix. The book begins with introducing fundamental nature of the charge conservation law associated with asymptotic symmetry, and explaining its relations to soft theorems and memory effect. Subsequently it looks into an appropriate asymptotic state of the S-matrix without infrared divergences. The Faddeev-Kulish dressed state is known as a candidate of such a state, and its gauge invariant condition and its relation to the asymptotic symmetry are discussed. It offers an important building blocks for constructing the S-matrix without infrared divergences.


Fifteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg15 Meeting On General Relativity (In 3 Volumes)

Fifteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg15 Meeting On General Relativity (In 3 Volumes)

Author: Elia S Battistelli

Publisher: World Scientific

Published: 2022-05-10

Total Pages: 2281

ISBN-13: 9811258260

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The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity.


Book Synopsis Fifteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg15 Meeting On General Relativity (In 3 Volumes) by : Elia S Battistelli

Download or read book Fifteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg15 Meeting On General Relativity (In 3 Volumes) written by Elia S Battistelli and published by World Scientific. This book was released on 2022-05-10 with total page 2281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity.


Dialogues Between Physics and Mathematics

Dialogues Between Physics and Mathematics

Author: Mo-Lin Ge

Publisher: Springer Nature

Published: 2022-12-10

Total Pages: 324

ISBN-13: 3031175239

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This volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry. Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.


Book Synopsis Dialogues Between Physics and Mathematics by : Mo-Lin Ge

Download or read book Dialogues Between Physics and Mathematics written by Mo-Lin Ge and published by Springer Nature. This book was released on 2022-12-10 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry. Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.


Einstein Equations: Physical and Mathematical Aspects of General Relativity

Einstein Equations: Physical and Mathematical Aspects of General Relativity

Author: Sergio Cacciatori

Publisher: Springer Nature

Published: 2019-11-23

Total Pages: 359

ISBN-13: 3030180611

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This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.


Book Synopsis Einstein Equations: Physical and Mathematical Aspects of General Relativity by : Sergio Cacciatori

Download or read book Einstein Equations: Physical and Mathematical Aspects of General Relativity written by Sergio Cacciatori and published by Springer Nature. This book was released on 2019-11-23 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.


Black Hole Information and Thermodynamics

Black Hole Information and Thermodynamics

Author: Dieter Lüst

Publisher: Springer

Published: 2019-01-25

Total Pages: 116

ISBN-13: 3030109194

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Based on Prof. Lüst's Masters course at the University of Munich, this book begins with a short introduction to general relativity. It then presents black hole solutions, and discusses Penrose diagrams, black hole thermodynamics and entropy, the Unruh effect, Hawking radiation, the black hole information problem, black holes in supergravity and string theory, the black hole microstate counting in string theory, asymptotic symmetries in general relativity, and a particular quantum model for black holes. The book offers an up-to-date summary of all the pertinent questions in this highly active field of physics, and is ideal reading for graduate students and young researchers.


Book Synopsis Black Hole Information and Thermodynamics by : Dieter Lüst

Download or read book Black Hole Information and Thermodynamics written by Dieter Lüst and published by Springer. This book was released on 2019-01-25 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on Prof. Lüst's Masters course at the University of Munich, this book begins with a short introduction to general relativity. It then presents black hole solutions, and discusses Penrose diagrams, black hole thermodynamics and entropy, the Unruh effect, Hawking radiation, the black hole information problem, black holes in supergravity and string theory, the black hole microstate counting in string theory, asymptotic symmetries in general relativity, and a particular quantum model for black holes. The book offers an up-to-date summary of all the pertinent questions in this highly active field of physics, and is ideal reading for graduate students and young researchers.


Effective Field Theories For Nuclei And Compact-star Matter: Chiral Nuclear Dynamics (Cnd-iii)

Effective Field Theories For Nuclei And Compact-star Matter: Chiral Nuclear Dynamics (Cnd-iii)

Author: Rho Mannque

Publisher: World Scientific

Published: 2018-10-23

Total Pages: 380

ISBN-13: 981327333X

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Effective field theories have been widely used in nuclear physics. This volume is devoted to exploring the intricate structure of compact-star matter inaccessible directly from QCD. It is principally anchored on hidden symmetries and topology presumed to be encoded in QCD. It differs from standard effective field theory and energy density functional approaches in that it exploits renormalization-group flow in the complex 'vacuum' sliding with density inferred from topology change identified as a manifestation of baryon-quark continuity in dense matter. It makes a variety of predictions that drastically differ from the conventional treatments that could be tested by upcoming terrestrial and astrophysical experiments.This monograph recounts how to go, in one unique field theoretic formalism in terms of hadronic degrees of freedom, from finite nuclei to dense compact-star matter that could be explored in RIB-type machines in nuclear physics as well as in LIGO-type gravity waves in astrophysics.


Book Synopsis Effective Field Theories For Nuclei And Compact-star Matter: Chiral Nuclear Dynamics (Cnd-iii) by : Rho Mannque

Download or read book Effective Field Theories For Nuclei And Compact-star Matter: Chiral Nuclear Dynamics (Cnd-iii) written by Rho Mannque and published by World Scientific. This book was released on 2018-10-23 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective field theories have been widely used in nuclear physics. This volume is devoted to exploring the intricate structure of compact-star matter inaccessible directly from QCD. It is principally anchored on hidden symmetries and topology presumed to be encoded in QCD. It differs from standard effective field theory and energy density functional approaches in that it exploits renormalization-group flow in the complex 'vacuum' sliding with density inferred from topology change identified as a manifestation of baryon-quark continuity in dense matter. It makes a variety of predictions that drastically differ from the conventional treatments that could be tested by upcoming terrestrial and astrophysical experiments.This monograph recounts how to go, in one unique field theoretic formalism in terms of hadronic degrees of freedom, from finite nuclei to dense compact-star matter that could be explored in RIB-type machines in nuclear physics as well as in LIGO-type gravity waves in astrophysics.


Lie Theory and Its Applications in Physics

Lie Theory and Its Applications in Physics

Author: Vladimir Dobrev

Publisher: Springer Nature

Published: 2020-10-15

Total Pages: 552

ISBN-13: 9811577757

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This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.


Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.


Jacob Bekenstein: The Conservative Revolutionary

Jacob Bekenstein: The Conservative Revolutionary

Author: Brink Lars

Publisher: World Scientific

Published: 2019-09-12

Total Pages: 392

ISBN-13: 9811203970

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Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entropy.Moreover, he found that their entropy was not extensive, unlike that of any other thermodynamical system considered before, but rather is proportional to the surface of their horizon. Furthermore, Bekenstein pioneered the study of black holes by focusing on their information content aspects. This led him to obtain bounds of a holographic nature on the amount of information that can be stored in a given region of space-time.This book contains a series of scientific and personal contributions by his contemporaries who recall the struggle against his ideas and then with them: the fate accompanying many revolutionary ideas. This is followed by original scientific contributions by many of the leaders of current research on black hole physics and holography. They have trodden his path and expanded it. The impact of Jacob Bekenstein's visionary ideas is just starting to be understood.


Book Synopsis Jacob Bekenstein: The Conservative Revolutionary by : Brink Lars

Download or read book Jacob Bekenstein: The Conservative Revolutionary written by Brink Lars and published by World Scientific. This book was released on 2019-09-12 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entropy.Moreover, he found that their entropy was not extensive, unlike that of any other thermodynamical system considered before, but rather is proportional to the surface of their horizon. Furthermore, Bekenstein pioneered the study of black holes by focusing on their information content aspects. This led him to obtain bounds of a holographic nature on the amount of information that can be stored in a given region of space-time.This book contains a series of scientific and personal contributions by his contemporaries who recall the struggle against his ideas and then with them: the fate accompanying many revolutionary ideas. This is followed by original scientific contributions by many of the leaders of current research on black hole physics and holography. They have trodden his path and expanded it. The impact of Jacob Bekenstein's visionary ideas is just starting to be understood.