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Questions in Quantum Physics: a Personal View
Questions in quantum physics: a personal view Rudolf Haag Waldschmidtstraße 4b, D–83727 Schliersee-Neuhaus, Germany Abstract An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical structure of the theory. 1 Introduction Personal views are shaped by past experiences and so it may be worth while pondering a little about accidental circumstances which channelled the course of one’s own thinking. Meeting the right person at the right time, stumbling across a book or article which suddenly opens a new window. Fifty years ago, as eager students at Munich University just entering the phase of our own scientific research, we were studying the enormous papers by Julian Schwinger on Quantum Electrodynamics, following the arguments line by line but not really grasping the message. I remember the feelings of frustration, realizing that we were far away from the centers of action. But, mixed with this, also some dismay which did not only refer to the enormous arsenal of formalism in the new arXiv:hep-th/0001006v1 3 Jan 2000 developments of QED but began with the standard presentation of the interpretation of Quantum Theory. I remember long discussions with my thesis advisor Fritz Bopp, often while circling some blocks of streets ten times late in the evening, where we looked in vain for some reality behind the enigma of wave-particle dualism. Why should physical quantities correspond to operators in Hilbert space? Why should probabilities be described as absolute squares of amplitudes?, etc., etc. -
From Algebraic Quantum Field Theory to Effective Quantum Gravity
Algebraic approach to QFT Quantum gravity Locality and beyond: from algebraic quantum field theory to effective quantum gravity Kasia Rejzner University of York Local Quantum Physics and beyond in memoriam Rudolf Haag, 26.09.2016 Kasia Rejzner Locality and beyond 1 / 26 Algebraic approach to QFT Quantum gravity Outline of the talk 1 Algebraic approach to QFT AQFT LCQFT pAQFT 2 Quantum gravity Effective quantum gravity Observables The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). Kasia Rejzner Locality and beyond 2 / 26 One of the fathers of LQP. We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. Kasia Rejzner Locality and beyond 2 / 26 We will all miss him. AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. Kasia Rejzner Locality and beyond 2 / 26 AQFT Algebraic approach to QFT LCQFT Quantum gravity pAQFT The father of Local Quantum Physics Rudolf Haag (1922 – 2016). The author of a beautiful book Local Quantum Physics. One of the fathers of LQP. We will all miss him. Kasia Rejzner Locality and beyond 2 / 26 It started as the axiomatic framework of Haag-Kastler[ Haag & Kastler 64]: a model is defined by associating to each region O of Minkowski spacetime the algebra A(O) of observables that can be measured in O. -
Spring 2019 Fine Letters
Spring 2019 • Issue 8 Department of MATHEMATICS Princeton University From the Chair Professor Allan Sly Receives MacArthur Fellowship Congratulations to Sly works on an area of probability retical computer science, where a key the Class of 2019 theory with applications from the goal often is to understand whether and all the finishing physics of magnetic materials to it is likely or unlikely that a large set graduate students. computer science and information of randomly imposed constraints on a Congratulations theory. His work investigates thresh- system can be satisfied. Sly has shown to the members of olds at which complex networks mathematically how such systems of- class of 2018 and suddenly change from having one ten reach a threshold at which solving new Ph. D.s who set of properties to another. Such a particular problem shifts from likely are reading Fine Letters for the first questions originally arose in phys- or unlikely. Sly has used a party invi- time as alumni. As we all know, the ics, where scientists observed such tation list as an analogy for the work: Math major is a great foundation for shifts in the magnetism of certain As you add interpersonal conflicts a diverse range of endeavors. This metal alloys. Sly provided a rigorous among a group of potential guests, it is exemplified by seventeen '18's who mathematical proof of the shift and can suddenly become effectively im- have gone to industry and seventeen a framework for identifying when possible to create a workable party. to grad school; ten to advanced study such shifts occur. -
Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz
FUNDAMENTALS OF PHYSICS – Vol. I - Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz QUANTUM MECHANICAL LAWS Bogdan Mielnik and Oscar Rosas-Ortiz Departamento de Física, Centro de Investigación y de Estudios Avanzados, México Keywords: Indeterminism, Quantum Observables, Probabilistic Interpretation, Schrödinger’s cat, Quantum Control, Entangled States, Einstein-Podolski-Rosen Paradox, Canonical Quantization, Bell Inequalities, Path integral, Quantum Cryptography, Quantum Teleportation, Quantum Computing. Contents: 1. Introduction 2. Black body radiation: the lateral problem becomes fundamental. 3. The discovery of photons 4. Compton’s effect: collisions confirm the existence of photons 5. Atoms: the contradictions of the planetary model 6. The mystery of the allowed energy levels 7. Luis de Broglie: particles or waves? 8. Schrödinger’s wave mechanics: wave vibrations explain the energy levels 9. The statistical interpretation 10. The Schrödinger’s picture of quantum theory 11. The uncertainty principle: instrumental and mathematical aspects. 12. Typical states and spectra 13. Unitary evolution 14. Canonical quantization: scientific or magic algorithm? 15. The mixed states 16. Quantum control: how to manipulate the particle? 17. Measurement theory and its conceptual consequences 18. Interpretational polemics and paradoxes 19. Entangled states 20. Dirac’s theory of the electron as the square root of the Klein-Gordon law 21. Feynman: the interference of virtual histories 22. Locality problems 23. The idea UNESCOof quantum computing and future – perspectives EOLSS 24. Open questions Glossary Bibliography Biographical SketchesSAMPLE CHAPTERS Summary The present day quantum laws unify simple empirical facts and fundamental principles describing the behavior of micro-systems. A parallel but different component is the symbolic language adequate to express the ‘logic’ of quantum phenomena. -
Numdam:AIHPA 1996__64 4 385 0
ANNALES DE L’I. H. P., SECTION A RUDOLF HAAG IZUMI OJIMA On the problem of defining a specific theory within the frame of local quantum physics Annales de l’I. H. P., section A, tome 64, no 4 (1996), p. 385-393 <http://www.numdam.org/item?id=AIHPA_1996__64_4_385_0> © Gauthier-Villars, 1996, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. Inst. Henri Poincare, Vol. 64, n° 4, 1996, 385 Physique theorique On the problem of defining a specific theory within the frame of local quantum physics Rudolf HAAG Waldschmidtstraße 4B D-83727 Schliersee, Germany. Izumi OJIMA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan. ABSTRACT. - The notion and use of germs of states are discussed. La notion de germe d’état et son utilisation sont 1’ objet de cette discussion. 1. INTRODUCTION The customary procedure of defining a specific theory or model in Quantum Field Theory starts by writing down a Lagrangean in terms of point-like fields. This defines first of all a classical field theory which is then subjected to a process called "quantization", either in the old fashioned form of replacing the numerical-valued fields by field operators with commutation relations or by a Feynman-Schwinger functional integral which should directly give the correlation functions of fields in the vacuum state. -
Laudatio for Michael Aizenman NAW 5/4 Nr
Aernout van Enter, Frank den Hollander Laudatio for Michael Aizenman NAW 5/4 nr. 2 juni 2003 107 Aernout van Enter Frank den Hollander Instituut voor theoretische natuurkunde Eurandom Rijksuniversiteit Groningen Technische Universiteit Eindhoven Nijenborgh 4, 9747 AG Groningen Postbus 513, 5600 MB Eindhoven [email protected] [email protected] Laudatio Laudatio for Michael Aizenman Eens per drie jaar reikt het Wiskundig Ge- Michael is the author of seventy-five research or ‘down’) or as particles (‘occupied’ or ‘emp- nootschap in opdracht van de Koninklijke Ne- papers in journals of mathematics, physics ty’). Their finite-volume conditional distribu- derlandse Academie van Wetenschappen de and mathematical physics. He has collaborat- tions (i.e., the probabilities of events inside a Brouwermedaille uit aan een internationaal ed with many co-authors on a broad range of finite volume given the state outside) are pre- toonaangevend onderzoeker. Hij wordt uit- topics. Much of his work is inspired by proba- scribed by a nearest-neighbor interaction that genodigd om een voordracht te geven op het bility theory and statistical physics, both clas- tends to ‘align spins’ or ‘glue together parti- Nederlands Mathematisch Congres, waar na sical and quantum. In his papers he typically cles’ and that contains the temperature as a afloop de laureaat de Brouwermedaille wordt ‘rides several horses at the same time’, in the parameter. At low temperature and in two uitgereikt. In 2002 werd de medaille toege- sense that cross-fertilization between differ- or more dimensions, there exists more than kend aan Michael Aizenman voor zijn bijdra- ent areas in physics and mathematics is at one infinite-volume probability measure hav- ge aan de mathematische fysica. -
A Life in Statistical Mechanics Part 1: from Chedar in Taceva to Yeshiva University in New York
Eur. Phys. J. H 42, 1–21 (2017) DOI: 10.1140/epjh/e2017-80006-9 THE EUROPEAN PHYSICAL JOURNAL H Oral history interview A life in statistical mechanics Part 1: From Chedar in Taceva to Yeshiva University in New York Joel L. Lebowitz1,a and Luisa Bonolis2,b 1 Departments of Mathematics and Physics, Rutgers, The State University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA 2 Max Planck Institute for the History of Science, Boltzmannstrasse 22, 14195 Berlin, Germany Received 10 February 2017 / Accepted 10 February 2017 Published online 4 April 2017 c The Author(s) 2017. This article is published with open access at Springerlink.com Abstract. This is the first part of an oral history interview on the life- long involvement of Joel Lebowitz in the development of statistical mechanics. Here the covered topics include the formative years, which overlapped the tragic period of Nazi power and World War II in Eu- rope, the emigration to the United States in 1946 and the schooling there. It also includes the beginnings and early scientific works with Peter Bergmann, Oliver Penrose and many others. The second part will appear in a forthcoming issue of Eur. Phys. J. H. 1 From war ravaged Europe to New York L. B. Let’s start from the very beginning. Where were you born? J. L. I was born in Taceva, a small town in the Carpathian mountains, in an area which was at that time part of Czechoslovakia, on the border of Romania and about a hundred kilometers from Poland. That was in 1930, and the town then had a population of about ten thousand people, a small town, but fairly advanced. -
09W5055 Statistical Mechanics on Random Structures
09w5055 Statistical Mechanics on Random Structures Anton Bovier (Rheinische Friedrich-Wilhelms-Universitat¨ Bonn), Pierluigi Contucci (University of Bologna), Frank den Hollander (University of Leiden and EURANDOM), Cristian Giardina` (TU Eindhoven and EURANDOM). 15 November - 20 November 2009 1 Overview of the Field The theme of the workshop has been equilibrium and non-equilibrium statistical mechanics in a random spatial setting. Put differently, the question was what happens when the world of interacting particle systems is put together with the world of disordered media. This area of research is lively and thriving, with a constant flow of new ideas and exciting developments, in the best of the tradition of mathematical physics. Spin glasses were at the core of the program, but in a broad sense. Spin glass theory has found ap- plications in a wide range of areas, including information theory, coding theory, algorithmics, complexity, random networks, population genetics, epidemiology and finance. This opens up many new challenges to mathematics. 2 Recent Developments and Open Problems The workshop brought together researchers whose interest lies at the intersection of disordered statistical mechanics and random graph theory, with a clear emphasis on applications. The multidisciplinary nature of the proposed topics has attracted research groups with different backgrounds and thus provided exchange of ideas with cross-fertilisation. As an example, we mention two problems on which we focused during the workshop. The first problem has its origin in the many fundamental issues that are still open in the theory of spin glasses. Even tough today we have a rigorous proof, in the context of mean-field models, of the solution for the free energy first proposed by G. -
A Mathematical Physicist's Perspective on Statistical Mechanics
A mathematical physicist’s perspective on Statistical Mechanics Michael Aizenman Princeton University André Aisenstadt Lecture (I) CRM, Montreal Sept. 24, 2018 1 /14 Statistical mechanics explains and quantifies the process by which structure emerges from chaos. Its genesis is in Boltzmann’s explanation of thermodynamical behavior and in particular of the concept of entropy. The statistic mechanical perspective was instrumental for Planck’s theory of the light quantization and Einstein’s calculation of the Avogadro number. More recent developments include links between the physics of critical phenomena and the mathematics of conformally invariant random structures, stochastic integrability, and representation theory. The talk will focus on examples of observations and conjectures which turned out to point in fruitful directions. 2 /14 Statistical Mechanics: laws emerging from chaos Laws expressed in equations F = ma, E = mc2, PV = nRT . A bird of a seemingly different feather: ∆S ≥ 0 . Q: what is entropy? L. Boltzmann: Thermodynamics emerges from Statistical Mechanics! Stat-Mech starts with a quantification of chaos: S = kB log W StatMech perspective was embraced and used for further developments by: M. Planck ) quantum theory of light (surmised from the black body radiation) A. Einstein ) Avogadro number from Brownian motion (exp. Perrin) −itH R. Feynman ) path representation of quantum dynamics: Ψt = e Ψ0 J. Wheeler: “There is no law except the law that there is no law.” Paraphrased: all physics laws are emergent features. 3 /14 Statistical Mechanics: laws emerging from chaos Laws expressed in equations F = ma, E = mc2, PV = nRT . A bird of a seemingly different feather: ∆S ≥ 0 . Q: what is entropy? L. -
V.Y. Glaser SOME RETROSPECTIVE REMARKS by Ph. Blanchard
V.Y. Glaser SOME RETROSPECTIVE REMARKS by Ph. Blanchard OPENINGS MATHEMATICS IN PHYSICS GREAT ENCOUNTERS ALONG THE WAY Zagreb, Göttingen, Copenhagen, Geneva, Strasbourg, Bures sur Yvette USING MATHEMATICS WITH CLARITY AND ELEGANCE Quantum Mechanics, Quantum Field Theory O P E N I N G S I am happy to have been asked to speak about Yurko Glaser, his thinking and its actions. It is an honor for me to pay tribute to the brilliant achievements of this leading mathematical physicist, gifted teacher and exceptional friend. It was in Strasbourg at the spring meeting of the RCP 25, where we first met 1967. At this time I was in Zürich at the ETH, working on the Paul-Fierz model of the infrared catastrophe under the direction of Res Jost. Yurko was born on April 21, 1924 just before the discovery by Schrödinger, Heisenberg, Dirac, Born … of modern Quantum Theory in the mid 1920’s. Carlo Rubbia was also born in Gorizia, Görz, Friaul – Julisch Venetien. Quantum Theory before 1925 – the Old Quantum Theory (Planck, Einstein, Bohr, Sommerfeld …) – was part craft part art. Old principles had been founded wanting, new ones had not yet been discovered. Modern Quantum Theory was a real revolution of our understanding of physical process. Compared with this change, Einstein’s relativity, born in 1905, seem not much more than very interesting variations on nevertheless classical themes. Yurko studied at the University of Zagreb, where he received his Diploma in 1950 and his Ph.D in 1953 under the supervision of W. Heisenberg. He moved to Göttingen in 1951-1952 and made his first important contributions to physics, a book of QED published 1955 in Zagreb and outstanding results on QFT, the attempt to clarify the compatibility of special relativity theory with Quantum Theory. -
On Spin Systems with Quenched Randomness: Classical and Quantum
On Spin Systems with Quenched Randomness: Classical and Quantum Rafael L. Greenblatt(a) ∗ Michael Aizenman(b) y Joel L. Lebowitz(c)∗ (a) Department of Physics and Astronomy Rutgers University, Piscataway NJ 08854-8019, USA (b) Departments of Physics and Mathematics Princeton University, Princeton NJ 08544, USA (a) Departments of Mathematics and Physics Rutgers University, Piscataway NJ 08854-8019, USA December 5, 2009 Dedicated to Nihat Berker on the occasion of his 60th birthday Abstract The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d ≤ 2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d ≤ 4. Some questions concerning the behavior of related order parameters in such random systems are discussed. 1 Introduction The effect of quenched randomness on the equilibrium and transport properties of macroscopic systems is a subject of great theoretical and practical interest which is close to Nihat’s heart. He and his collaborators [1, 2, 3] made important contributions to the study of the changes brought about by such randomness in phase transitions occurring in the pure (non-random) system. These effects can be profound in low dimensions. Their understanding evolved in a somewhat interesting way. -
An Introduction to Rigorous Formulations of Quantum Field Theory
An introduction to rigorous formulations of quantum field theory Daniel Ranard Perimeter Institute for Theoretical Physics Advisors: Ryszard Kostecki and Lucien Hardy May 2015 Abstract No robust mathematical formalism exists for nonperturbative quantum field theory. However, the attempt to rigorously formulate field theory may help one understand its structure. Multiple approaches to axiomatization are discussed, with an emphasis on the different conceptual pictures that inspire each approach. 1 Contents 1 Introduction 3 1.1 Personal perspective . 3 1.2 Goals and outline . 3 2 Sketches of quantum field theory 4 2.1 Locality through tensor products . 4 2.2 Schr¨odinger(wavefunctional) representation . 6 2.3 Poincar´einvariance and microcausality . 9 2.4 Experimental predictions . 12 2.5 Path integral picture . 13 2.6 Particles and the Fock space . 17 2.7 Localized particles . 19 3 Seeking rigor 21 3.1 Hilbert spaces . 21 3.2 Fock space . 23 3.3 Smeared fields . 23 3.4 From Hilbert space to algebra . 25 3.5 Euclidean path integral . 30 4 Axioms for quantum field theory 31 4.1 Wightman axioms . 32 4.2 Haag-Kastler axioms . 32 4.3 Osterwalder-Schrader axioms . 33 4.4 Consequences of the axioms . 34 5 Outlook 35 6 Acknowledgments 35 2 1 Introduction 1.1 Personal perspective What is quantum field theory? Rather than ask how nature truly acts, simply ask: what is this theory? For a moment, strip the physical theory of its interpretation. What remains is the abstract mathematical arena in which one performs calculations. The theory of general relativity becomes geometry on a Lorentzian manifold; quantum theory becomes the analysis of Hilbert spaces and self-adjoint operators.