Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories
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Symmetry and Gravity
universe Article Making a Quantum Universe: Symmetry and Gravity Houri Ziaeepour 1,2 1 Institut UTINAM, CNRS UMR 6213, Observatoire de Besançon, Université de Franche Compté, 41 bis ave. de l’Observatoire, BP 1615, 25010 Besançon, France; [email protected] or [email protected] 2 Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking GU5 6NT, UK Received: 05 September 2020; Accepted: 17 October 2020; Published: 23 October 2020 Abstract: So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has SUpN Ñ 8q – area preserving Diff.pS2q symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference—observer—and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Geometrodynamics of Gauge Fields on the Geometry of Yang-Mills and Gravitational Gauge Theories
springer.com Physics : Classical and Quantum Gravitation, Relativity Theory Mielke, Eckehard W. Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories A comprehensive revision of a classic text relating geometic field theory to modern physics Offers an up-to-date overview of geometrodynamics including minimal topological models Contains new chapters on teleparalelism, Chern-Simons-induced topological 3D gravity and supergravity, quantization via topological ghosts, constrained BF model with SL (5, R) gauge group, and chiral and trace anomalies Provides a detailed exposition of frame bundles in gravity Springer This monograph aims to provide a unified, geometrical foundation of gauge theories of 2nd ed. 2017, XVII, 373 p. elementary particle physics. The underlying geometrical structure is unfolded in a coordinate- 2nd 18 illus., 8 illus. in color. free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics edition such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It Printed book provides the framework in which the (broken) Poincarégauge theory, the Rainich geometrization Hardcover of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are Printed book developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be Hardcover exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de ISBN 978-3-319-29732-3 Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is £ 109,99 | CHF 141,50 | 119,99 € | presented. -
Symmetries and Pre-Metric Electromagnetism
Symmetries and pre-metric electromagnetism ∗ D.H. Delphenich ∗∗ Physics Department, Bethany College, Lindsborg, KS 67456, USA Received 27 April 2005, revised 14 July 2005, accepted 14 July 2005 by F. W. Hehl Key words Pre-metric electromagnetism, exterior differential systems, symmetries of differential equations, electromagnetic constitutive laws, projective relativity. PACS 02.40.k, 03.50.De, 11.30-j, 11.10-Lm The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed and then specialized to various possible forms for an electromagnetic constitutive law, namely, uniform linear, non-uniform linear, and uniform nonlinear. It is shown that in the uniform linear case, one has four possible ways of prolonging the symmetry Lie algebra, including prolongation to a Lie algebra of infinitesimal projective transformations of a real four-dimensional projective space. In the most general non-uniform linear case, the effect of non-uniformity on symmetry seems inconclusive in the absence of further specifics, and in the uniform nonlinear case, the overall difference from the uniform linear case amounts to a deformation of the electromagnetic constitutive tensor by the electromagnetic field strengths, which induces a corresponding deformation of the symmetry Lie algebra that was obtained in the linear uniform case. Contents 1 Introduction 2 2 Exterior differential systems 4 2.1 Basic concepts. ………………………………………………………………………….. 4 2.2 Exterior differential systems on Λ2(M). …………………………………………………. 6 2.3 Canonical forms on Λ2(M). ………………………………………………………………. 7 3. Symmetries of exterior differential systems 10 3.1 Basic concepts. -
Selected Papers on Teleparallelism Ii
SELECTED PAPERS ON TELEPARALLELISM Edited and translated by D. H. Delphenich Table of contents Page Introduction ……………………………………………………………………… 1 1. The unification of gravitation and electromagnetism 1 2. The geometry of parallelizable manifold 7 3. The field equations 20 4. The topology of parallelizability 24 5. Teleparallelism and the Dirac equation 28 6. Singular teleparallelism 29 References ……………………………………………………………………….. 33 Translations and time line 1928: A. Einstein, “Riemannian geometry, while maintaining the notion of teleparallelism ,” Sitzber. Preuss. Akad. Wiss. 17 (1928), 217- 221………………………………………………………………………………. 35 (Received on June 7) A. Einstein, “A new possibility for a unified field theory of gravitation and electromagnetism” Sitzber. Preuss. Akad. Wiss. 17 (1928), 224-227………… 42 (Received on June 14) R. Weitzenböck, “Differential invariants in EINSTEIN’s theory of teleparallelism,” Sitzber. Preuss. Akad. Wiss. 17 (1928), 466-474……………… 46 (Received on Oct 18) 1929: E. Bortolotti , “ Stars of congruences and absolute parallelism: Geometric basis for a recent theory of Einstein ,” Rend. Reale Acc. dei Lincei 9 (1929), 530- 538...…………………………………………………………………………….. 56 R. Zaycoff, “On the foundations of a new field theory of A. Einstein,” Zeit. Phys. 53 (1929), 719-728…………………………………………………............ 64 (Received on January 13) Hans Reichenbach, “On the classification of the new Einstein Ansatz on gravitation and electricity,” Zeit. Phys. 53 (1929), 683-689…………………….. 76 (Received on January 22) Selected papers on teleparallelism ii A. Einstein, “On unified field theory,” Sitzber. Preuss. Akad. Wiss. 18 (1929), 2-7……………………………………………………………………………….. 82 (Received on Jan 30) R. Zaycoff, “On the foundations of a new field theory of A. Einstein; (Second part),” Zeit. Phys. 54 (1929), 590-593…………………………………………… 89 (Received on March 4) R. -
Metric–Affine Gauge Theory of Gravity II. Exact Solutions Abstract
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Metric–affine gauge theory of gravity II. Exact solutions Friedrich W. Hehl∗ and Alfredo Mac´ıas† Departamento de F´ısica Universidad Aut´onoma Metropolitana–Iztapalapa Apartado Postal 55–534, C.P. 09340, M´exico, D.F., Mexico Abstract In continuing our series on metric-affine gravity (see Gronwald, IJMP D6 (1997) 263 for Part I), we review the exact solutions of this theory. file magexac7.tex, 1999-04-09 Typeset using REVTEX ∗E-mail: [email protected]. Permanent address: Institute for Theoretical Physics, University of Cologne, D–50923 K¨oln, Germany †E-mail: [email protected] 1 I. METRIC–AFFINE GRAVITY (MAG) In 1976, a new metric–affine theory of gravitation was published [16]. In this model, k the metric gij and the linear (sometimes also called affine) connection Γij were considered to be independent gravitational field variables. The metric carries 10 and the connection 64 independent components. Although nowadays more general Lagrangians are considered, like the one in Eq.(10), the original Lagrangian density of metric–affine gravity reads √ g = − gij Ric (Γ,∂Γ) + βQQ . (1) VGR0 2κ ij i j h i The Ricci tensor Ric ij depends only on the connection but not on the metric, whereas the Weyl covector Q := gkl g /4 depends on both. Here represents the covariant i − ∇i kl ∇i k derivative with respect to the connection Γij , furthermore g =detgkl, κ is Einstein’s gravitational constant, and β a dimensionless coupling constant. -
Molecular Symmetry
Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) – used with group theory to predict vibrational spectra for the identification of molecular shape, and as a tool for understanding electronic structure and bonding. Symmetrical : implies the species possesses a number of indistinguishable configurations. 1 Group Theory : mathematical treatment of symmetry. symmetry operation – an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. symmetry elements – the points, lines, or planes to which a symmetry operation is carried out. Element Operation Symbol Identity Identity E Symmetry plane Reflection in the plane σ Inversion center Inversion of a point x,y,z to -x,-y,-z i Proper axis Rotation by (360/n)° Cn 1. Rotation by (360/n)° Improper axis S 2. Reflection in plane perpendicular to rotation axis n Proper axes of rotation (C n) Rotation with respect to a line (axis of rotation). •Cn is a rotation of (360/n)°. •C2 = 180° rotation, C 3 = 120° rotation, C 4 = 90° rotation, C 5 = 72° rotation, C 6 = 60° rotation… •Each rotation brings you to an indistinguishable state from the original. However, rotation by 90° about the same axis does not give back the identical molecule. XeF 4 is square planar. Therefore H 2O does NOT possess It has four different C 2 axes. a C 4 symmetry axis. A C 4 axis out of the page is called the principle axis because it has the largest n . By convention, the principle axis is in the z-direction 2 3 Reflection through a planes of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produced an indistinguishable configuration, the symmetry element is called a mirror plane or plane of symmetry . -
Gabriele Veneziano
Strings 2021, June 21 Discussion Session High-Energy Limit of String Theory Gabriele Veneziano Very early days (1967…) • Birth of string theory very much based on the high-energy (Regge) limit: Im A(Regge) ≠ 0! •Duality bootstrap (except for the Pomeron!) => DRM (emphasis shifted on res/res duality, xing) •Need for infinite number of resonances of unlimited mass and spin (linear traj.s => strings?) • Exponential suppression @ high E & fixed θ => colliding objects are extended, soft (=> strings?) •One reason why the NG string lost to QCD. •Q: What’s the Regge limit of (large-N) QCD? 20 years later (1987…) •After 1984, attention in string theory shifted from hadronic physics to Q-gravity. • Thought experiments conceived and efforts made to construct an S-matrix for gravitational scattering @ E >> MP, b < R => “large”-BH formation (RD-3 ~ GE). Questions: • Is quantum information preserved, and how? • What’s the form and role of the short-distance stringy modifications? •N.B. Computations made in flat spacetime: an emergent effective geometry. What about AdS? High-energy vs short-distance Not the same even in QFT ! With gravity it’s even more the case! High-energy, large-distance (b >> R, ls) •Typical grav.al defl. angle is θ ~ R/b = GE/b (D=4) •Scattering at high energy & fixed small θ probes b ~ R/θ > R & growing with energy! •Contradiction w/ exchange of huge Q = θ E? No! • Large classical Q due to exchange of O(Gs/h) soft (q ~ h/b) gravitons: t-channel “fractionation” • Much used in amplitude approach to BH binaries • θ known since ACV90 up to O((R/b)3), universal. -
Arxiv:1910.10745V1 [Cond-Mat.Str-El] 23 Oct 2019 2.2 Symmetry-Protected Time Crystals
A Brief History of Time Crystals Vedika Khemania,b,∗, Roderich Moessnerc, S. L. Sondhid aDepartment of Physics, Harvard University, Cambridge, Massachusetts 02138, USA bDepartment of Physics, Stanford University, Stanford, California 94305, USA cMax-Planck-Institut f¨urPhysik komplexer Systeme, 01187 Dresden, Germany dDepartment of Physics, Princeton University, Princeton, New Jersey 08544, USA Abstract The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the per- petuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization (MBL). Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics — that of an intrinsically out-of-equilibrium many-body phase of matter with no equilibrium counterpart. We include a compendium of the necessary background on the statistical mechanics of phase structure in many- body systems, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. In particular, we provide precise definitions that formalize the notion of a time-crystal as a stable, macroscopic, conservative clock — explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. Our discussion emphasizes that TTSB in a time-crystal is accompanied by the breaking of a spatial symmetry — so that time-crystals exhibit a novel form of spatiotemporal order. -
Differentiable Manifolds
Gerardo F. Torres del Castillo Differentiable Manifolds ATheoreticalPhysicsApproach Gerardo F. Torres del Castillo Instituto de Ciencias Universidad Autónoma de Puebla Ciudad Universitaria 72570 Puebla, Puebla, Mexico [email protected] ISBN 978-0-8176-8270-5 e-ISBN 978-0-8176-8271-2 DOI 10.1007/978-0-8176-8271-2 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011939950 Mathematics Subject Classification (2010): 22E70, 34C14, 53B20, 58A15, 70H05 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.birkhauser-science.com) Preface The aim of this book is to present in an elementary manner the basic notions related with differentiable manifolds and some of their applications, especially in physics. The book is aimed at advanced undergraduate and graduate students in physics and mathematics, assuming a working knowledge of calculus in several variables, linear algebra, and differential equations. -
Arxiv:Cond-Mat/0006280V1 19 Jun 2000 H Ulda Group Euclidean the Fdsoain.Frhroe H Oino Ilcto Shgl Dissip Highly Is Dislocation Point of the Motion Damping)
Dislocation theory as a 3-dimensional translation gauge theory∗ Markus Lazar† Max-Planck-Institut f¨ur Metallforschung Institut f¨ur Physik D–70569 Stuttgart, Germany (November 1, 2018) We consider the static elastoplastic theory of dislocations in an elastoplastic ma- terial. We use a Yang-Mills type Lagrangian (the teleparallel equivalent of Hilbert- Einstein Lagrangian) and some Lagrangians with anisotropic constitutive laws. The translational part of the generalized affine connection is utilized to describe the the- ory of elastoplasticity in the framework of a translation gauge theory. We obtain a system of Yang-Mills field equations which express the balance of force and moment. Keywords: Dislocation theory; force stress; moment stress to appear in Annalen der Physik (2000) I. INTRODUCTION The field theory of defects in crystals has an old history. First, Kondo [1] and Bilby et al. [2] described independently a dislocation theory in the language of differential geometry. They proved the equivalence of dislocation density to Cartan’s torsion. Kr¨oner and Seeger [3,4] completed this theory to a non-linear theory of elasticity with dislocations and internal stress. Recent develop- ments of this theory are given in [5,6]. The first step towards a gauge theory of defects had been taken by Turski [7]. He derived the equilibrium equations by means of a variational principle. Edelen et al. [8,9] developed a theory of dislocations and disclinations as a gauge theory of the Euclidean group SO(3)×⊃ T (3) and a pure dislocation theory as a translational or T (3)-gauge theory. Unfortunately, they did not distinguish between disclinations in solid and in liquid crystals. -
Extreme Gravity and Fundamental Physics
Extreme Gravity and Fundamental Physics Astro2020 Science White Paper EXTREME GRAVITY AND FUNDAMENTAL PHYSICS Thematic Areas: • Cosmology and Fundamental Physics • Multi-Messenger Astronomy and Astrophysics Principal Author: Name: B.S. Sathyaprakash Institution: The Pennsylvania State University Email: [email protected] Phone: +1-814-865-3062 Lead Co-authors: Alessandra Buonanno (Max Planck Institute for Gravitational Physics, Potsdam and University of Maryland), Luis Lehner (Perimeter Institute), Chris Van Den Broeck (NIKHEF) P. Ajith (International Centre for Theoretical Sciences), Archisman Ghosh (NIKHEF), Katerina Chatziioannou (Flatiron Institute), Paolo Pani (Sapienza University of Rome), Michael Pürrer (Max Planck Institute for Gravitational Physics, Potsdam), Thomas Sotiriou (The University of Notting- ham), Salvatore Vitale (MIT), Nicolas Yunes (Montana State University), K.G. Arun (Chennai Mathematical Institute), Enrico Barausse (Institut d’Astrophysique de Paris), Masha Baryakhtar (Perimeter Institute), Richard Brito (Max Planck Institute for Gravitational Physics, Potsdam), Andrea Maselli (Sapienza University of Rome), Tim Dietrich (NIKHEF), William East (Perimeter Institute), Ian Harry (Max Planck Institute for Gravitational Physics, Potsdam and University of Portsmouth), Tanja Hinderer (University of Amsterdam), Geraint Pratten (University of Balearic Islands and University of Birmingham), Lijing Shao (Kavli Institute for Astronomy and Astro- physics, Peking University), Maaretn van de Meent (Max Planck Institute for Gravitational