DOCSLIB.ORG

Quantum Physics, Quantum Spacetime and Quantum Geometry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Physics, Quantum Spacetime and Quantum Geometry Quantum Physics, Quantum Spacetime and Quantum Geometry Sergio Doplicher Universit`adi Roma \Sapienza" February 16, 2016 Colloquium "Levi - Civita", 17 Febbraio 2016 1. Why Quantum 2. Why Quantum Spacetime 3. Quantum Minkowski Space 4. Quantum Geometry 5. QFT on QST 6. Comments on QST and Cosmology 1 Why Quantum 2 In a physical theory, the observable quantities are described by the selfad- joint elements in a C* Algebra A (a Banach * algebra s.t. jjA∗Ajj = jjAjj2; equivalently a uniformly closed * algebra of linear bounded operators on a Hilbert space); the physical states are described by states of that alge- bra (i.e. positive normalized linear functionals) and the expectation value of the observable A in the state ! is given by !(A). 3 Thus the uncertainty of A in ! is (∆A)2 =< (A− < A > I)2 > : If AB = BA, then A and B are compatible; otherwise, in any state of the system, ∆A∆B & (1=2)j < AB − BA > j: (Elementary consequence of Schwarz's inequality for the positive semidefinite sesquilinear form assigning to A; B the number !(A∗B)). If the C* Algebra generated by the observables is com- mutative, it can be identified with C0(Ω) for some lo- cally compact space Ω, the phase space of a Classical Theory. Noncommutativity of A is equivalent to the presence of any (hence of all) the following properties: 1. There is a pair of observables which cannot be mea- sured simultaneously. 2. There is an observable A and a pure state where A does not take a precise value (Quantum fluctuations). 3. There are pairs of distinct pure states which can be superposed, giving rise to a pure state distinct from both. 4. there exists a pair of distinct pure states with a nonzero transition probability from each to the other. 5. While time evolution in deterministic, measuring some observable in some pure state produces a state which is no longer pure. Thus commutativity characterizes Classical Theories, Noncommutatity is the sole responsible of the unintu- itive features of Quantum Mechanics. Is this choice a "capriccio" or even a "stravaganza"? NO. It was IMPOSED on us by Nature, after nearly 30 years of misunderstandings of what Nature was telling us. Is QM relevant only at the atomic scale?NO: - Superconductors (LHC); - Specific heat of metals, ambient temperatures; - The largest system we can think of, CMB, is a Quan- tum System. A word on the "Black body problem" is here in order. 4 (S.M.McMurry: Quantum Mechanics, Addison - Wesley, 1994). 6 Thus classically equilibrium matter - radiation was im- possible! Great failure of Classical Physics at the end of the XIX Century. CMB = Black Body radiation at T = 2:725 degrees Kelvin, temperature fluctuations 0.0002 degree, angu- lar size = that of a full Moon. Horizon Problem Solved by inflation hypothesis, but also by Quantum Spacetime. How did the Quantum picture of the World emerge? ** To explain the experimental curve of the spectrum of the black body radiation we had to assume that (Planck, 1900): the energy of a one dimensional harmonic oscillator of frequency ν can only take values which are integral mul- tiples of hν (h = Planck constant). ** To explain the photoelectric effect we had to assume that (Einstein, 1905): Electromagnetic Radiation of frequency ν consists of an integer number of indivisible units (photons) of energy hν. ** To explain why matter is stable and with a discrete spectrum of spectral lines (while the Planetary Model of atoms, confirmed by the Rutherford experiment (1911), would be instable, with continuos emission / absorption spectra according to Classical Physics!) we had to as- sume that: Bohr (1911 - 1924): Atomic bound states have (as Planck's oscillator) a discrete set of energy levels, the conservation of energy is respected in jumps by emission / absorption of a single photon: En − Em = hνnm This would explain the discrete nature of the observed emission / absorption spectra (hence would explain why we see colors!), and stability of atoms. BUT WHY? Dramatic wreck in Classical Physics. The answer was somehow implicit in the famous three 1905 papers of Einstein! The photon is indivisible like a particle, but is governed by a wave equation (Maxwell Equations)! If the electron, as the photon, is also governed by a wave equation, discrete energy levels arise as the dis- crete serie of frequencies produced by a vibrating string. Schroedinger equation. But: a bullet shot through an open window does not feel the window; while a wave gets diffracted going through an opening in a dam. Thus precision in one component of the coordinates im- plies imprecision in the same component of the speed. And, for the electron too, the precision in one compo- nent of the coordinates would imply imprecision in the same component of the momentum. Ideed: Heisenberg (1927): assigning a point in phase space to an electron has NO operational meaning: in any mea- surement process which is actually at least conceptually possible, we must have: ∆q∆p & ~ (~ = Planck constant per unit radiant). (The three 1905 papers by Einstein included that on Special Relativity. Key point: Operational definition of physical quantities to criticize the notion of simultane- ity. Heisenberg analysis took up that lesson 22 years later!) Can this fact be implemented by a precise mathematical scheme? Yes: pq − qp = −i~ (Born; Born and Jordan; Born, Heisenberg and Jordan, 1925; gives precise mathematical shape to Quantum Conditions invented by Heisenberg). Dirac (1926 - 1930): (Heisenberg - Born - Jordan and Schroedinger approaches are just special representa- tions of a new picture, where:) Observables are de- scribed by Operators (selfadjoint operators acting on a Hilbert space); spectrum = possible values; discrete spectrum and continuos spectrum; for the Energy Op- erator (Hamiltonian) the discrete spectrum describes BOUND STATES. The assumptions of Planck and of Bohr, stability of atoms, discrete emission - absorption spectra, . explained! The lesson that Nature was whispering in those nearly 30 years eventually understood. Modern view: the observables are selfadjoint elements of a C* algebra, Hilbert spaces arise as representation spaces (e.g. determined by a state, GNS construction). Heart of QM: Uncertainty Relations as a shadow of Noncommutativity. Probabilistic aspects are a consequence. Copernicus; Darwin; Freud; Quantum Mechanics! LAWS OF NATURE; Naturalism; Ethics and primacy of Culture. Why QST QM finitely many d. o. f. ∆q∆p & ~ positions = observables, dual to momentum; in QFT, local observables: A 2 A(O); O (double cones) - spacetime specifications, in terms of coordinates - accessible through measurements of local observables. Allows to formulate LOCALITY: 7 AB = BA whenever A 2 A(O1);B 2 A(O2; ); and O1; O2 are spacelike separated. "Unreasonable effectiveness”. OK at all accessible scales (down to 10−17cm:, LHC at CERN); in QFT at all scales, if we neglect GRAVITA- TIONAL FORCES BETWEEN ELEMENTARY PAR- TICLES. 8 If we DON'T: Heisenberg: localizing an event in a small region costs energy (QM); Einstein: energy generates a gravitational field (CGR). A strong gravitational field can generate "closed trapped surfaces". QM + CGR: PRINCIPLE OF Gravitational Stability against localization of events [DFR, 1994, 95]: The gravitational field generated by the concentra- tion of energy required by the Heisenberg Uncer- tainty Principle to localize an event in spacetime should not be so strong to hide the event itself to any distant observer - distant compared to the Planck scale. Spherically symmetric localization in space with accu- racy a: an uncontrollable energy E of order 1=a has to be transferred; Schwarzschild radius R ' E (in universal units where ~ = c = G = 1). 9 Hence we must have that a & R ' 1=a; so that a & 1; i.e. in CGS units −33 a & λP ' 1:6 · 10 cm: (1) (Planck length). (FOLKLORE). But elaborations in two significant directions are sur- prisingly recent. First, if we consider the energy content of a generic quantum state where the location measurement is per- formed, the bounds on the uncertainties should also depend upon that energy content. Second, if we consider generic uncertainties, the argu- ment above suggests that they ought to be limited by uncertainty relations. To the first point: background state: spherically symmetric distribution, total energy E within a sphere of radius R, with E < R. If we localize, in a spherically symmetric way, an event at the origin with space accuracy a, due to the Heisen- berg Principle the total energy will be of the order 1=a + E. Reasoning as above, we must then have 1 + E < R: a Thus, if R − E is much smaller than 1, the \minimal distance" will be much larger than 1. Indication that Quantum Spacetime solves the Horizon Problem. To the second point: The condition that closed trapped surfaces do not arise implies that the ∆qµ must satisfy UNCERTAINTY RELATIONS. Should be implemented by commutation relations, making spacetime into a QUANTUM SPACETIME. Dependence of Uncertainty Relations, hence of Com- mutators between coordinates, upon background quan- tum state i.e. upon metric tensor. Hard problem. CGR: Geometry ∼ Dynamics QG: Algebra ∼ Dynamics WARNING: Size of the known Universe: 1028cm. Planck scale: much further away from us in log scale. QM: no contradiction from the size of the Universe (CMB is a quantum system!) down to scales explored by LHC. Below that scale no direct experimental knowledge. GR: no contradiction from the size of the Universe down to scales of order 10−2cm. Below, nothing is known. The (Planck length), 10−33cm, is very far. Quantum Minkowski Space The Principle of Gravitational Stability against localization of events implies : 3 X X ∆q0 · ∆qj & 1; ∆qj∆qk & 1: (2) j=1 1≤j<k≤3 [DFR 1994 - 95]; see also [TV 2012] [DMP 2013] Must be implemented by SPACETIME commutation relations 10 2 [qµ; qν] = iλP Qµν (3) imposing Quantum Conditions on the Qµν.
Load more

Recommended publications
  • Perturbative Algebraic Quantum Field Theory
    Perturbative algebraic quantum field theory Klaus Fredenhagen Katarzyna Rejzner II Inst. f. Theoretische Physik, Department of Mathematics, Universität Hamburg, University of Rome Tor Vergata Luruper Chaussee 149, Via della Ricerca Scientifica 1, D-22761 Hamburg, Germany I-00133, Rome, Italy [email protected] [email protected] arXiv:1208.1428v2 [math-ph] 27 Feb 2013 2012 These notes are based on the course given by Klaus Fredenhagen at the Les Houches Win- ter School in Mathematical Physics (January 29 - February 3, 2012) and the course QFT for mathematicians given by Katarzyna Rejzner in Hamburg for the Research Training Group 1670 (February 6 -11, 2012). Both courses were meant as an introduction to mod- ern approach to perturbative quantum field theory and are aimed both at mathematicians and physicists. Contents 1 Introduction 3 2 Algebraic quantum mechanics 5 3 Locally covariant field theory 9 4 Classical field theory 14 5 Deformation quantization of free field theories 21 6 Interacting theories and the time ordered product 26 7 Renormalization 26 A Distributions and wavefront sets 35 1 Introduction Quantum field theory (QFT) is at present, by far, the most successful description of fundamental physics. Elementary physics , to a large extent, explained by a specific quantum field theory, the so-called Standard Model. All the essential structures of the standard model are nowadays experimentally verified. Outside of particle physics, quan- tum field theoretical concepts have been successfully applied also to condensed matter physics. In spite of its great achievements, quantum field theory also suffers from several longstanding open problems. The most serious problem is the incorporation of gravity.
    [Show full text]
  • A Scale-Covariant Quantum Space-Time
    A scale-covariant quantum space-time Claudio Perini∗ Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, PA 16802-6300, USA Gabriele Nunzio Tornetta† School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Scotland A noncommutative space-time admitting dilation symmetry was briefly mentioned in the seminal work [1] of Doplicher, Fredenhagen and Roberts. In this paper we explicitly construct the model in details and carry out an in-depth analysis. The C∗-algebra that describes this quantum space-time is determined, and it is shown that it admits an action by - automorphisms of the dilation group, along with the expected Poincar´ecovariance. In order∗ to study the main physical properties of this scale-covariant model, a free scalar neutral field is introduced as a investigation tool. Our key results are then the loss of locality and the irreducibility, or triviality, of special field algebras associated with regions of the ordinary Minkowski space-time. It turns out, in the conclusions, that this analysis allows also to argue on viable ways of constructing a full conformally covariant model for quantum space-time. I. INTRODUCTION In this paper we study a non-commutative space-time of DFR-type, that can be obtained as the limiting scale-free case of the original DFR model [1]. The main mathematical interest to study this model is that it is Poincar´e and dilation covariant, thus it possesses almost all the symmetries given by the conformal group. The issue of implementing the remaining symmetry, which is the relativistic ray inversion, is discussed in the concluding section.
    [Show full text]
  • Arxiv:1306.6519V5 [Math-Ph] 13 May 2014 5.1 Vacuum State
    Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics Klaus Fredenhagen and Falk Lindner II. Institute for Theoretical Physics, University of Hamburg [email protected], [email protected] Abstract We present a general construction of KMS states in the framework of pertur- bative algebraic quantum field theory (pAQFT). Our approach may be understood as an extension of the Schwinger-Keldysh formalism. We obtain in particular the Wightman functions at positive temperature, thus solving a problem posed some time ago by Steinmann [55]. The notorious infrared divergences observed in a di- agrammatic expansion are shown to be absent due to a consequent exploitation of the locality properties of pAQFT. To this avail, we introduce a novel, Hamiltonian description of the interacting dynamics and find, in particular, a precise relation between relativistic QFT and rigorous quantum statistical mechanics. Dedicated to the memory of Othmar Steinmann ∗27.11.1932 †11.03.2012 Contents 1 Introduction 2 2 Perturbed dynamics 4 3 Time averaged Hamiltonian description of the dynamics 7 4 KMS states for the interacting dynamics: General discussion 13 4.1 The case of finite volume . 13 4.2 The case of infinite volume . 17 5 Cluster properties of the massive scalar field 19 arXiv:1306.6519v5 [math-ph] 13 May 2014 5.1 Vacuum state . 20 5.2 Thermal equilibrium states . 23 6 Conclusion 29 A Proof of the KMS condition 31 1 B Propositions for the adiabatic limit 34 1 Introduction According to the standard model of cosmology, the early universe was for some time in an equilibrium state with high temperature.
    [Show full text]
  • Dark Matter and Weak Signals of Quantum Spacetime
    PHYSICAL REVIEW D 95, 065009 (2017) Dark matter and weak signals of quantum spacetime † ‡ Sergio Doplicher,1,* Klaus Fredenhagen,2, Gerardo Morsella,3, and Nicola Pinamonti4,§ 1Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 2II Institut für Theoretische Physik, Universität Hamburg, D-22761 Hamburg, Germany 3Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy 4Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy, and INFN Sezione di Genova, Genova, Italy (Received 29 December 2016; published 13 March 2017) In physically motivated models of quantum spacetime, a Uð1Þ gauge theory turns into a Uð∞Þ gauge theory; hence, free classical electrodynamics is no longer free and neutral fields may have electromagnetic interactions. We discuss the last point for scalar fields, as a way to possibly describe dark matter; we have in mind the gravitational collapse of binary systems or future applications to self-gravitating Bose-Einstein condensates as possible sources of evidence of quantum gravitational phenomena. The effects considered so far, however, seem too faint to be detectable at present. DOI: 10.1103/PhysRevD.95.065009 I. INTRODUCTION but their superpositions would, in general, not be—they would lose energy in favor of mysterious massive modes One of the main difficulties of present-day physics is the (see also [6]). lack of observation of quantum aspects of gravity. Quantum A naive computation showed, by that mechanism, that a gravity has to be searched without a guide from nature; the monochromatic wave train passing through a partially observed universe must be explained as carrying traces of reflecting mirror should lose, in favor of those ghost quantum gravitational phenomena in the only “laboratory” modes, a fraction of its energy—a very small fraction, suitable to those effects, i.e., the universe itself a few unfortunately, of the order of one part in 10−130 [5].
    [Show full text]
  • The Principle of Locality. Effectiveness, Fate and Challenges
    The Principle of Locality. Effectiveness, fate and challenges Sergio Doplicher Dipartimento di Matematica University of Rome “La Sapienza” 00185 Roma, Italy October 26, 2018 Abstract The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of Quantum Field Theory, especially in absence of massless particles. This effectiveness shows up best in the formulation of Quantum Field Theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of Global Gauge Invariance, through the analysis of Superselection Structure and Statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the Principle of Local Gauge Invariance. This problem emerges also if one attempts to figure out the fate of the Principle of Locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localisation of events, of the notion of Spacetime, shows that, in the small, the latter must loose arXiv:0911.5136v1 [math-ph] 26 Nov 2009 any meaning as a classical pseudoRiemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the Geometry of a basic model of Quantum Spacetime and some attempts to formulate interaction of quantum fields on Quan- tum Spacetime. The Principle of Locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely a Prin- ciple where the General Theory of Relativity and Quantum Mechanics merge, which reduces to the Principle of Locality at larger scales.
    [Show full text]
  • Adiabatic Limits and Renormalization in Quantum Spacetime
    DOTTORATO DI RICERCA IN MATEMATICA XXXII CICLO DEL CORSO DI DOTTORATO Adiabatic limits and renormalization in quantum spacetime Aleksei Bykov A.A. 2019/2020 Docente Guida/Tutor: Prof. D. Guido Relatore: Prof. G. Morsella Coordinatore: Prof. A. Braides Contents 1 Introduction 4 2 Doplicher-Fredenhagen-Roberts Quantum Spacetime 11 2.1 Construction and basic facts . 11 2.2 Quantum fields on the DFR QST and the role of Qµν . 12 2.2.1 More general quantum fields in DFR QST . 13 2.3 Optimally localised states and the quantum diagonal map . 17 3 Perturbation theory for QFT and its non-local generalization 21 3.1 Hamiltonian perturbation theory . 22 3.1.1 Ordinary QFT . 22 3.1.2 Non-local case: fixing HI ............................. 26 3.1.3 Hamiltonian approach: fixing Hint ........................ 35 3.2 Lagrangian perturbation theories . 38 3.3 Yang-Feldman quantizaion . 41 3.4 LSZ reduction . 41 4 Feynman rules for non-local Hamiltonian Perturbation theory 45 5 Lagrangian reformulation of the Hamiltonian Feynman rules 52 6 Corrected propagator 57 7 Adiabatic limit 61 7.1 Weak adiabatic limit and the LSZ reduction . 61 7.1.1 Existence of the weak adiabatic limit . 61 7.1.2 Feynman rules from LSZ reduction . 64 7.2 Strong adiabatic limit . 65 8 Renormalization 68 8.1 Formal renormalization . 68 8.2 The physical renormalization . 71 8.2.1 Dispersion relation renormalisation . 72 8.2.2 Field strength renormalization . 72 8.3 Conluding remarks on renormalisation . 73 9 Conclusions 75 9.1 Summary of the main results . 75 9.2 Outline of further directions .
    [Show full text]
  • Quantum Field Theory: Where We Are 3
    Quantum Field Theory: Where We Are Klaus Fredenhagen1, Karl-Henning Rehren2, and Erhard Seiler3 1 II. Institut f¨ur Theoretische Physik, Universit¨at Hamburg, 22761 Hamburg, Germany [email protected] 2 Institut f¨ur Theoretische Physik, Universit¨at G¨ottingen, 37077 G¨ottingen, Germany [email protected] 3 Max-Planck-Institut f¨ur Physik, 80805 M¨unchen, Germany [email protected] Summary. We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory. arXiv:hep-th/0603155v1 20 Mar 2006 1 Introduction Quantum field theory aims at a synthesis of quantum physics with the prin- ciples of classical field theory, in particular the principle of locality. Its main Contribution to: An Assessment of Current Paradigms in the Physics of Fun- damental Phenomena, to be published by Springer Verlag (2006). 2 Klaus Fredenhagen, Karl-Henning Rehren, and Erhard Seiler realm is the theory of elementary particles where it led to a far reaching under- standing of the structure of physics at subatomic scales with an often amaz- ingly good agreement between theoretical predictions and experiments. Typ- ical observables in QFT are current densities or energy flow densities which correspond to what is measured in particle physics detectors. The original aim of QFT was to compute expectation values and correlation functions of the observables, and to derive scattering cross sections in high-energy physics. In the course of development, QFT has widened its scope, notably towards the inclusion of gravitational interactions.
    [Show full text]
  • Operator Algebras and Applications, Volume 38-Part 1
    http://dx.doi.org/10.1090/pspum/038.1 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume 38, Part 1 OPERATOR ALGEBRAS AND APPLICATIONS AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1982 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT QUEENS UNIVERSITY KINGSTON, ONTARIO JULY 14-AUGUST 2, 1980 EDITED BY RICHARD V. KADISON Prepared by the American Mathematical Society with partial support from National Science Foundation grant MCS 79-27061 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics (1980: Queens University, Kingston, Ont.) Operator algebras and applications. (Proceedings of symposia in pure mathematics; v. 38) Includes bibliographies and index. 1. Operator algebras-Congresses. I. Kadison, Richard V., 1925— II. Title. III. Series. QA326.S95 1982 512'.55 82-11561 ISBN 0-8218-1441-9 (v. 1) ISBN 0-8218-1444-3 (v. 2) ISBN 0-8218-1445-1 (set) 1980 Mathematics Subject Classification. Primary 46L05, 46L10; Secondary 43A80, 81E05, 82A15. Copyright © 1982 by the American Mathematical Society Printed in the United States of America All rights reserved except those granted to the United States Government. This book may not be reproduced in any form without the permission of the publishers. TABLE OF CONTENTS PARTI Author index xi Preface RICHARD V. KADISON xvn* Operator algebras—the first forty years 1 RICHARD V. KADISON On the structure theory of C*-algebras: some old and new problems 19 EDWARD G. EFFROS Homological invariants of extensions of C*-algebras 35 JONATHAN ROSENBERG Geometric resolutions and the Kunneth formula for C*-algebras 77 CLAUDE SCHOCHET The J£-groups for free products of C*-algebras 81 JOACHIM CUNTZ The internal structure of simple C*-algebras 85 JOACHIM CUNTZ K homology and index theory 117 PAUL BAUM AND RONALD G.
    [Show full text]
  • Rudolf Haag's Legacy of Local Quantum Physics And
    Rudolf Haag’s legacy of Local Quantum Physics and reminiscences about a cherished teacher and friend In memory of Rudolf Haag (1922-2016) submitted to the Eur. Phys. J. H Bert Schroer permanent address: Institut f¨ur Theoretische Physik FU-Berlin, Arnimallee 14, 14195 Berlin, Germany November 2016 Abstract After some personal recollectioms about Rudolf Haag and his thoughts which led him to ”Local Quantum Physics”, the present work recalls his ideas about scattering theory, the relation between local observables and localized fields and his contributions to the physical aspects of modu- lar operator theory which paved the way for an intrisic understanding of quantum causal localization in which fields ”coordinatize” the local algebras. The paper ends with the presentation of string-local fields whose con- struction and use in a new renormalization theory for higher spin fields is part of an ongoing reformulation of gauge theory in the conceptual setting of Haag’s LQP. 1 First encounter with Rudolf Haag arXiv:1612.00003v1 [math-ph] 30 Nov 2016 On his return from the Niels Bohr Institute in Copenhagen to the University of Munich Rudolf Haag passed through Hamburg to meet his colleague Harry Lehmann, at that time the newly appointed successor of Wilhelm Lenz who held the chair of theoretical physics since the 1920 foundation of the University of Hamburg. It was the year 1958 shortly after the decision to construct the DESY particle accelerator in Hamburg which created a lot of excitement. I had nearly completed my diploma thesis under Lehmann and begun to worry about my career.
    [Show full text]
  • Aspects of Holography and Quantum Error Correction by Pratik Rath a Dissertation Submitted in Partial Satisfaction of the Requir
    Aspects of Holography And Quantum Error Correction by Pratik Rath A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Yasunori Nomura, Chair Professor Raphael Bousso Professor Richard Borcherds Summer 2020 Aspects of Holography And Quantum Error Correction Copyright 2020 by Pratik Rath 1 Abstract Aspects of Holography And Quantum Error Correction by Pratik Rath Doctor of Philosophy in Physics University of California, Berkeley Professor Yasunori Nomura, Chair The holographic principle has been a central theme in most of the progress in the field of quantum gravity in recent years. Our understanding of the AdS/CFT duality, the best known embodiment of the holographic principle, has taken a quantum leap in the last decade. A key role in the elucidation of how the holographic duality functions has been played by ideas from quantum information theory. In particular, the modern understanding of the holographic dictionary is that it works as a quantum error correcting code. In this dissertation, we focus on a two-pronged approach to developing a deeper insight into the framework of quantum gravity. Firstly, despite the fact that we have learnt a lot about quantum gravity from AdS/CFT, it is not directly applicable to our universe which is an accelerating cosmological spacetime. Taking inspiration from the holographic principle and formulating ideas from AdS/CFT in the abstract language of quantum error correction, we take some preliminary steps in freeing ourselves from the crutches of AdS spacetimes and understanding features of holography in a wider class of spacetimes.
    [Show full text]
  • Advances in Algebraic Quantum Field Theory
    Advances in Algebraic Quantum Field Theory Klaus Fredenhagen II. Institut f¨urTheoretische Physik, Hamburg Klaus Fredenhagen Advances in Algebraic Quantum Field Theory Embedding of physical systems into larger systems requires characterization of subsystems understanding relations between subsystems (independence versus determinism, correlations, entanglement) Characterization of subsystems by their material content (\a system of two electrons") turns out to be problematic: Particle number not well defined during interaction Because of nontrivial particle statistics systems with n particles cannot identified in a natural way as subsystems of a system with m > n particles (e.g. Hanbury Brown Twist effect: Photons from different sources are entangled) Klaus Fredenhagen Advances in Algebraic Quantum Field Theory Haag (1957): Algebras of observables measurable in some finitely extended region of spacetime are good subsystems. Needs an a priori notion of spacetime and therefore cannot directly be applied to quantum gravity, but turned out to cover the essence of relativistic quantum field theory, in particular due to the stability of this concept in time because of the finite velocity of light. In nonrelativistic physics the identification of an algebra which is invariant under time evolution for an interesting dynamics is more difficult. (see no go theorems by Narnhofer and Thirring and the recent work of Buchholz (resolvent algebra) for progress). Klaus Fredenhagen Advances in Algebraic Quantum Field Theory Haag-Kastler Axioms Haag's concept of algebras of local observables can be summarized as follows: A quantum system is represented by a C*-algebra with unit, i.e. an algebra with unit over the complex numbers with an antilinear involution A 7! A∗ and a norm which satisfies the condition jjA∗Ajj = jjAjj2 such that the algebra is complete with respect to the induced topology.
    [Show full text]
  • History of RSB Interview: Francesco Guerra January 26, 2021, 8:30Am-10:30Pm (EST)
    History of RSB Interview: Francesco Guerra January 26, 2021, 8:30am-10:30pm (EST). Final revision: May 10, 2021 Interviewers: Patrick Charbonneau, Duke University, [email protected] Francesco Zamponi, ENS-Paris Location: Over Zoom, from Prof. Guerra’s second home in Genova, Italy. How to cite: P. Charbonneau, History of RSB Interview: Francesco Guerra, transcript of an oral history conducted 2021 by Patrick Charbonneau and Francesco Zamponi, History of RSB Project, CAPHÉS, École normale supérieure, Paris, 2021, 27 p. https://doi.org/10.34847/nkl.05bd6npc PC: Hello, Professor Guerra. Thank you very much for joining us. As we've dis- cussed, today we will be mostly discussing the history of replica symmetry breaking in a broad sense. Before we get there, however, we wanted to ask you a few questions about your background and interests. In particular, could you tell us what led you to be interested in physics and to pursue a Laurea degree in theoretical physics? FG: Like many people in Italy, in the first two years of university I was enrolled in engineering, like Ettore Majorana1 for example. Then I found that I was more interested in basic scientific questions, so I decided to shift to phys- ics. It was the start in Naples at the time—it was ‘62—of new, big enter- prises in physics. In Naples, there was the old institute of physics and they were involved mostly in classical physics, spectroscopy, solid state physics, and so on. Then, in the middle of the ‘50s, modern physics underwent an impressive development. My big boss at the time was Eduardo Caianiello2.
    [Show full text]