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Arxiv:2004.05668V2 [Hep-Th] 9 Jun 2020
A note on electric-magnetic duality and soft charges Marc Henneaux,a;b;1 Cédric Troessaertc aUniversité Libre de Bruxelles and International Solvay Institutes, Physique Mathématique des Interactions Fondamentales, Campus Plaine—CP 231, Bruxelles B-1050, Belgium bCollège de France, 11 place Marcelin Berthelot, 75005 Paris, France cHaute-Ecole Robert Schuman, Rue Fontaine aux Mûres, 13b, B-6800, Belgium E-mail: [email protected], [email protected] Abstract: We derive the asymptotic symmetries of the manifestly duality invariant for- mulation of electromagnetism in Minkoswki space. We show that the action is invariant under two algebras of angle-dependent u(1) transformations, one electric and the other magnetic. As in the standard electric formulation, Lorentz invariance requires the addition of additional boundary degrees of freedom at infinity, found here to be of both electric and magnetic types. A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators are equal to only half of the electric and magnetic fluxes (the other half is brought in by Dirac- string type contributions). Another notable feature is the absence of central extension in the angle-dependent u(1)2-algebra. arXiv:2004.05668v2 [hep-th] 9 Jun 2020 1ORCID: 0000-0002-3558-9025 Contents 1 Introduction 1 2 Starting point 3 2.1 Action and presymplectic form 3 2.2 Hamiltonian vector fields 4 2.3 Boundary conditions 4 2.4 Improper gauge symmetries 5 2.5 Equations of motion 7 3 Poincaré -
Group Theory
Appendix A Group Theory This appendix is a survey of only those topics in group theory that are needed to understand the composition of symmetry transformations and its consequences for fundamental physics. It is intended to be self-contained and covers those topics that are needed to follow the main text. Although in the end this appendix became quite long, a thorough understanding of group theory is possible only by consulting the appropriate literature in addition to this appendix. In order that this book not become too lengthy, proofs of theorems were largely omitted; again I refer to other monographs. From its very title, the book by H. Georgi [211] is the most appropriate if particle physics is the primary focus of interest. The book by G. Costa and G. Fogli [102] is written in the same spirit. Both books also cover the necessary group theory for grand unification ideas. A very comprehensive but also rather dense treatment is given by [428]. Still a classic is [254]; it contains more about the treatment of dynamical symmetries in quantum mechanics. A.1 Basics A.1.1 Definitions: Algebraic Structures From the structureless notion of a set, one can successively generate more and more algebraic structures. Those that play a prominent role in physics are defined in the following. Group A group G is a set with elements gi and an operation ◦ (called group multiplication) with the properties that (i) the operation is closed: gi ◦ g j ∈ G, (ii) a neutral element g0 ∈ G exists such that gi ◦ g0 = g0 ◦ gi = gi , (iii) for every gi exists an −1 ∈ ◦ −1 = = −1 ◦ inverse element gi G such that gi gi g0 gi gi , (iv) the operation is associative: gi ◦ (g j ◦ gk) = (gi ◦ g j ) ◦ gk. -
Asymptotic Structure of Electromagnetism and Gravity in The
Asymptotic structure of elec- tromagnetism and gravity in the asymptotically flat case Marc Henneaux Introduction Asymptotic structure of electromagnetism and The problem in a nutshell - Electromagnetism gravity in the asymptotically flat case New boundary conditions Gravity Conclusions and Marc Henneaux comments Geometry and Duality Workshop, AEI, Potsdam - 6 December 2019 1 / 33 Asymptotic symmetries play a central role in holographic duality. This is familiar from the AdS/CFT context, where the asymptotic symmetry group (which is infinite-dimensional in the case of AdS3 gravity) is the group of rigid symmetries of the dual boundary theory. What is the situation in the asymptotically flat context ? This will be the subject of this talk. Introduction Asymptotic structure of elec- tromagnetism and gravity in the asymptotically flat case Marc Henneaux Introduction The problem in a nutshell - Electromagnetism New boundary conditions Gravity Conclusions and comments 2 / 33 This is familiar from the AdS/CFT context, where the asymptotic symmetry group (which is infinite-dimensional in the case of AdS3 gravity) is the group of rigid symmetries of the dual boundary theory. What is the situation in the asymptotically flat context ? This will be the subject of this talk. Introduction Asymptotic structure of elec- tromagnetism and gravity in the asymptotically flat case Marc Henneaux Introduction Asymptotic symmetries play a central role in holographic duality. The problem in a nutshell - Electromagnetism New boundary conditions Gravity Conclusions and comments 2 / 33 What is the situation in the asymptotically flat context ? This will be the subject of this talk. Introduction Asymptotic structure of elec- tromagnetism and gravity in the asymptotically flat case Marc Henneaux Introduction Asymptotic symmetries play a central role in holographic duality. -
Hypersymmetric Black Holes in 2+1 Gravity
Hypersymmetric black holes in 2+1 gravity Marc Henneaux Introduction Three- dimensional pure gravity with ¤ 0 Ç Hypergravity Hypersymmetric black holes in 2+1 gravity Charges and asymptotic analysis Hypersymmetry Marc Henneaux bounds Black holes Conclusions ETH, November 2015 1 / 28 Supersymmetry is well known to have deep consequences. In the context of higher spin gauge theories, supersymmetry is generalized to include fermionic symmetries described by parameters of spin 3/2, 5/2 etc Do these symmetries also have interesting implications ? In particular, do they imply “hypersymmetry" bounds ? The answer turns out to be affirmative, as can be seen for instance by analysing anti-de Sitter hypergravity in 2 1 Å dimensions. Based on joint work with A. Pérez, D. Tempo, R. Troncoso (2015) Introduction Hypersymmetric black holes in 2+1 gravity Marc Henneaux Introduction Three- dimensional pure gravity with ¤ 0 Ç Hypergravity Charges and asymptotic analysis Hypersymmetry bounds Black holes Conclusions 2 / 28 In the context of higher spin gauge theories, supersymmetry is generalized to include fermionic symmetries described by parameters of spin 3/2, 5/2 etc Do these symmetries also have interesting implications ? In particular, do they imply “hypersymmetry" bounds ? The answer turns out to be affirmative, as can be seen for instance by analysing anti-de Sitter hypergravity in 2 1 Å dimensions. Based on joint work with A. Pérez, D. Tempo, R. Troncoso (2015) Introduction Hypersymmetric black holes in 2+1 gravity Marc Henneaux Introduction Supersymmetry is well known to have deep consequences. Three- dimensional pure gravity with ¤ 0 Ç Hypergravity Charges and asymptotic analysis Hypersymmetry bounds Black holes Conclusions 2 / 28 Do these symmetries also have interesting implications ? In particular, do they imply “hypersymmetry" bounds ? The answer turns out to be affirmative, as can be seen for instance by analysing anti-de Sitter hypergravity in 2 1 Å dimensions. -
Paul Langevin (1872-1946), La Relativité Et Les Quanta, Bulletin De La Société Française De Physique, N° 119, Mai 1999, 15-20
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Hal-Diderot M ICHEL P ATY LANGEVIN, LA RELATIVITE ET LES QUANTA 1 Paul Langevin (1872-1946), la relativité et les quanta, Bulletin de la Société Française de Physique, n° 119, mai 1999, 15-20. Paul Langevin (1872-1946), la relativité et les quanta Michel PATY* Formation et profil scientifique: entre l'expérience et la théorie.- Les nouveaux phénomènes sur la constitution des corps et le «fondement électromagnétique de la matière» - La théorie de la relativité restreinte interprétée comme dynamique électromagnétique. Les phénomènes quantiques.- L'interprétation de la mécanique quantique.- Mémoire de Langevin. “Résumer l'œuvre de Langevin, écrivait Louis de Broglie en 1947, c'est reprendre toute l'histoire de la physique depuis cinquante ans” 1. Aussi bien telle n'est pas l'intention de cet article. Mais cette remarque de son célèbre élève est propre à rappeler d'emblée la dimension de ce physicien considérable, qui était l'une des meilleures et des plus sûres têtes pensantes de son époque, et d'ailleurs pas seulement en physique. Mais c'est à la physique que nous nous limiterons ici, et même à l'évocation d'un aspect relativement circonscrit de son histoire: comment, et en quoi, ce physicien clairvoyant et profond que fut Paul Langevin s'est-il trouvé amené à prendre sa part des renouvellements radicaux qui ont transformé la physique au début du XXè siècle, à savoir la relativité et les quanta. Il nous faut commencer par rappeler quelques éléments de sa biographie, et surtout de sa formation2. -
Alternative Gravitational Theories in Four Dimensions
Alternative Gravitational Theories in Four Dimensionsa Friedrich W. Hehl Institute for Theoretical Physics, University of Cologne, D-50923 K¨oln, Germany email: [email protected] We argue that from the point of view of gauge theory and of an appropriate interpretation of the interferometer experiments with matter waves in a gravitational field, the Einstein- Cartan theory is the best theory of gravity available. Alternative viable theories are general relativity and a certain teleparallelism model. Objections of Ohanian & Ruffini against the Einstein-Cartan theory are discussed. Subsequently we list the papers which were read at the ‘Alternative 4D Session’ and try to order them, at least partially, in the light of the structures discussed. 1 The best alternative theory? I would call general relativity theory8 GR the best available alternative gravitational 21,14 theory and the next best one its teleparallel equivalent GR||. Because of these two theories, at least, it is good to have this alternative session during the Marcel Grossmann Meeting. Let me try to explain why I grant to GR the distinction of being the best alternative theory. After finally having set up special relativity theory in 1905, Einstein subse- quently addressed the question of how to generalize Newton’s gravitational theory as to make it consistent with special relativity, that is, how to reformulate it in a Poincar´ecovariant way. Newton’s theory was a battle tested theory in the realm of our planetary system and under normal laboratory conditions. It has predictive power as it had been shown by the prediction of the existence of the planet Neptune in the last century. -
Sur Ma Généalogie Scientifique Française
Sur ma g´en´ealogie scientifique fran¸caise Didier Henrion Octobre 2010 1 Motivation Durant l'´et´e2010 j'ai effectu´equelques recherches sur ma g´en´ealogiescientifique, afin de compl´eterla base de donn´ees[Mathematics Genealogy Project]. Dans ce document j'ai regroup´equelques informations sur le profil des scientifiques constituant ma branche g´en´ealogiquefran¸caise. Le 12 octobre 1999 j'ai obtenu ma th`esede doctorat fran¸caise[Henrion, 1999] de l'Institut National des Sciences Appliqu´ees(INSA) de Toulouse, devant un jury constitu´ede Christian Burgat (pr´esident), Luc Dugard, Michel Malabre (rapporteurs), Jacques Bernussou, Vladim´ırKuˇcera,Bernard Pradin (examinateurs) et Sophie Tar- bouriech (directrice de th`ese).Les travaux de th`esecombinaient des r´esultatsd'automatique dans la lign´ee des travaux d'Aleksandr Lyapunov (chercheur russe du d´ebutdu XX`emesi`ecle,contemporain d'Henri Poin- car´e,et pr´ecurseurde l'´etudedes syst`emesdynamiques), pour ´etudierla stabilit´ede syst`emeslin´eairesdont les actionneurs saturent, et des r´esultatsd'optimisation convexe et de math´ematiquesappliqu´ees,concernant les in´egalit´esmatricielles lin´eaires,particuli`erement adapt´ees`ala commande des syst`emesen pr´esenced'incertitudes param´etriqueset de mod´elisation. On notera la pr´esencedans le jury de th`esede Bernard Pradin, alors professeur d'automatique `al'INSA de Toulouse. Ses cours, ainsi que ceux de Germain Garcia, Christian Mira et Andr´eTitli, sont `al'origine de ma vocation. En 1998 j'ai ´egalement obtenu un doctorat de l'Acad´emiedes Sciences de la R´epubliqueTch`eque,mais je compte d´ecrirema g´en´ealogietch`equedans un autre document. -
Newton-Cartan Gravity Revisited Andringa, Roel
University of Groningen Newton-Cartan gravity revisited Andringa, Roel IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2016 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Andringa, R. (2016). Newton-Cartan gravity revisited. Rijksuniversiteit Groningen. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license. More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne- amendment. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 30-09-2021 1 Newton-Cartan gravity revisited Proefschrift ter verkrijging van de graad van doctor aan de Rijksuniversiteit Groningen op gezag van de rector magnificus prof. dr. E. -
A Scenario for Strong Gravity Without Extra Dimensions
A Scenario for Strong Gravity without Extra Dimensions D. G. Coyne (University of California at Santa Cruz) A different reason for the apparent weakness of the gravitational interaction is advanced, and its consequences for Hawking evaporation of a Schwarzschild black hole are investigated. A simple analytical formulation predicts that evaporating black holes will undergo a type of phase transition resulting in variously long-lived objects of reasonable sizes, with normal thermodynamic properties and inherent duality characteristics. Speculations on the implications for particle physics and for some recently-advanced new paradigms are explored. Section I. Motivation In the quest for grand unification of particle physics and gravitational interactions, the vast difference in the scale of the forces, gravity in particular, has long been a puzzle. In recent years, string theory developments [1] have suggested that the “extra” dimensions of that theory are responsible for the weakness of observed gravity, in a scenario where gravitons are unique in not being confined to a brane upon which the remaining force carriers are constrained to lie. While not a complete theory, such a scenario has interesting ramifications and even a prediction of sorts: if the extra dimensions are large enough, the Planck mass M = will be reduced to c G , G P hc GN h b b being a bulk gravitational constant >> GN. Black hole production at the CERN Large Hadron Collider is then predicted [2], together with the inability to probe high-energy particle physics at still higher energies and smaller distances. Experiments searching for consequences of the extra dimensions have not yet shown evidence for their existence, but have set upper limits on their characteristic sizes [3]. -
November 2019
A selection of some recent arrivals November 2019 Rare and important books & manuscripts in science and medicine, by Christian Westergaard. Flæsketorvet 68 – 1711 København V – Denmark Cell: (+45)27628014 www.sophiararebooks.com AMPÈRE, André-Marie. THE FOUNDATION OF ELECTRO- DYNAMICS, INSCRIBED BY AMPÈRE AMPÈRE, Andre-Marie. Mémoires sur l’action mutuelle de deux courans électri- ques, sur celle qui existe entre un courant électrique et un aimant ou le globe terres- tre, et celle de deux aimans l’un sur l’autre. [Paris: Feugeray, 1821]. $22,500 8vo (219 x 133mm), pp. [3], 4-112 with five folding engraved plates (a few faint scattered spots). Original pink wrappers, uncut (lacking backstrip, one cord partly broken with a few leaves just holding, slightly darkened, chip to corner of upper cov- er); modern cloth box. An untouched copy in its original state. First edition, probable first issue, extremely rare and inscribed by Ampère, of this continually evolving collection of important memoirs on electrodynamics by Ampère and others. “Ampère had originally intended the collection to contain all the articles published on his theory of electrodynamics since 1820, but as he pre- pared copy new articles on the subject continued to appear, so that the fascicles, which apparently began publication in 1821, were in a constant state of revision, with at least five versions of the collection appearing between 1821 and 1823 un- der different titles” (Norman). The collection begins with ‘Mémoires sur l’action mutuelle de deux courans électriques’, Ampère’s “first great memoir on electrody- namics” (DSB), representing his first response to the demonstration on 21 April 1820 by the Danish physicist Hans Christian Oersted (1777-1851) that electric currents create magnetic fields; this had been reported by François Arago (1786- 1853) to an astonished Académie des Sciences on 4 September. -
Hypergravity in Ads3
Physics Letters B 739 (2014) 106–109 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Hypergravity in AdS3 Yu.M. Zinoviev Institute for High Energy Physics, Protvino, Moscow Region, 142280, Russia a r t i c l e i n f o a b s t r a c t Article history: Thirty years ago Aragone and Deser showed that in three dimensions there exists a consistent model Received 19 August 2014 describing interaction for massless spin-2 and spin-5/2fields. It was crucial that these fields lived in Received in revised form 18 September a flat Minkowski space and as a result it was not possible to deform such model into anti-de Sitter 2014 space. In this short note we show that such deformation becomes possible provided one compliment Accepted 17 October 2014 to the model with massless spin-4 field. Resulting theory can be considered as a Chern–Simons one Available online 24 October 2014 with a well-known supergroup OSp(1, 4). Moreover, there exists a straightforward generalization to the Editor: L. Alvarez-Gaumé OSp(1, 2n) case containing a number of bosonic fields with even spins 2, 4, ..., 2n and one fermionic field with spin n + 1/2. © 2014 Published by Elsevier B.V. This is an open access article under the CC BY license 3 (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP . 1. Introduction and show that in AdS background it describes interacting system 5 of massless spin-2, spin-4 and spin- 2 fields. -
20 Gravitational Zoology: How Animals Use and Cope with Gravity
20 Gravitational Zoology: How Animals Use and Cope with Gravity Ralf H. Anken and Hinrich Rahmann Since the dawn of life on Earth some four billions of years ago, gravity has been a more or less stable environmental factor thus influencing the phylogenetic develop- ment of all living organisms. On the one side, gravity represents a factor of physical restriction, which compelled the ancestors of all extant living beings to develop basic achievements to counter the gravitational force (e.g., elements of statics like any kind of skeleton - from actin to bone - to overcome gravity enforced size limits or to keep form). On the other side, already early forms of life possibly used gravity as an appro- priate cue for orientation and postural control, since it is continuously present and has a fixed direction. Due to such a thorough adaptation to the Earthly gravity vector, both orientation behavior as well as the ontogenetic development of animals is impaired, when they have to experience altered gravity (Dg; i.e. hyper- or microgravity). Nevertheless, ani- mals still can cope with Dg in a certain range based on their physiological plasticity, which varies among the different animal phyla. 20.1 Gravity as a Factor of Physical Restriction: A Brief History of Evolutionary Challenges To Surmount It As a matter of fact, the non-linear self-organizing dynamics of biological systems are inherent in any physical theory that satisfies the requirements of both quantum me- chanics and general relativity [1]. Gravity therefore has always been a challenge for biological systems to adapt or/and to cope with it.