Zakopane Lectures on Loop Gravity
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Report of Contributions
2016 CAP Congress / Congrès de l’ACP 2016 Report of Contributions https://indico.cern.ch/e/CAP2016 2016 CAP Congr … / Report of Contributions **WITHDRAWN** Nanoengineeri … Contribution ID: 980 Type: Oral (Non-Student) / orale (non-étudiant) **WITHDRAWN** Nanoengineering materials: a bottom-up approach towards understanding long outstanding challenges in condensed matter science Thursday, 16 June 2016 08:30 (15 minutes) Chemists have made tremendous advances in synthesizing a variety of nanostructures with control over their size, shape, and chemical composition. Plus, it is possible to control their assembly and to make macroscopic materials. Combined, these advances suggest an opportunity to “nanoengineer” materials ie controllably fabricate materials from the nanoscale up with a wide range of controlled and potentially even new behaviours. Our group has been exploring this opportunity, and has found a rich range of material elec- tronic behaviours that even simple nano-building blocks can generate, e.g. single electron effects, metal-insulator transitions, semiconductor transistor-like conductance gating, and, most recently, strongly correlated electronic behaviour. The latter is particularly exciting. Strongly correlated electrons are known to lie at the heart of some of the most exotic, widely studied and still out- standing challenges in condensed matter science (e.g. high Tc superconductivity in the cuprates and others). The talk will survey both new insights and new opportunities that arise as a result of usingthis nanoengineering -
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. -
Conformal Symmetry in Field Theory and in Quantum Gravity
universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals). -
Large-D Behavior of the Feynman Amplitudes for a Just-Renormalizable Tensorial Group Field Theory
PHYSICAL REVIEW D 103, 085006 (2021) Large-d behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory † Vincent Lahoche1,* and Dine Ousmane Samary 1,2, 1Commissariatal ` ’Énergie Atomique (CEA, LIST), 8 Avenue de la Vauve, 91120 Palaiseau, France 2Facult´e des Sciences et Techniques (ICMPA-UNESCO Chair), Universit´ed’Abomey- Calavi, 072 BP 50, Benin (Received 22 December 2020; accepted 22 March 2021; published 16 April 2021) This paper aims at giving a novel approach to investigate the behavior of the renormalization group flow for tensorial group field theories to all order of the perturbation theory. From an appropriate choice of the kinetic kernel, we build an infinite family of just-renormalizable models, for tensor fields with arbitrary rank d. Investigating the large d-limit, we show that the self-energy melonic amplitude is decomposed as a product of loop-vertex functions depending only on dimensionless mass. The corresponding melonic amplitudes may be mapped as trees in the so-called Hubbard-Stratonivich representation, and we show that only trees with edges of different colors survive in the large d-limit. These two key features allow to resum the perturbative expansion for self energy, providing an explicit expression for arbitrary external momenta in terms of Lambert function. Finally, inserting this resummed solution into the Callan-Symanzik equations, and taking into account the strong relation between two and four point functions arising from melonic Ward- Takahashi identities, we then deduce an explicit expression for relevant and marginal β-functions, valid to all orders of the perturbative expansion. By investigating the solutions of the resulting flow, we conclude about the nonexistence of any fixed point in the investigated region of the full phase space. -
Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected]
Old Dominion University ODU Digital Commons Faculty-Sponsored Student Research Electrical & Computer Engineering 2017 Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected] Follow this and additional works at: https://digitalcommons.odu.edu/engineering_students Part of the Elementary Particles and Fields and String Theory Commons, Engineering Physics Commons, and the Quantum Physics Commons Repository Citation Daniels, Adam, "Unification of Gravity and Quantum Theory" (2017). Faculty-Sponsored Student Research. 1. https://digitalcommons.odu.edu/engineering_students/1 This Report is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted for inclusion in Faculty-Sponsored Student Research by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Unification of Gravity and Quantum Theory Adam D. Daniels [email protected] Electrical and Computer Engineering Department, Old Dominion University Norfolk, Virginia, United States Abstract- An overview of the four fundamental forces of objects falling on earth. Newton’s insight was that the force that physics as described by the Standard Model (SM) and prevalent governs matter here on Earth was the same force governing the unifying theories beyond it is provided. Background knowledge matter in space. Another critical step forward in unification was of the particles governing the fundamental forces is provided, accomplished in the 1860s when James C. Maxwell wrote down as it will be useful in understanding the way in which the his famous Maxwell’s Equations, showing that electricity and unification efforts of particle physics has evolved, either from magnetism were just two facets of a more fundamental the SM, or apart from it. -
Unification of Nature's Fundamental Forces
Unification of Nature’s Geoffrey B. West Fredrick M. Cooper Fundamental Forces Emil Mottola a continuing search Michael P. Mattis it was explicitly recognized at the time that basic research had an im- portant and seminal role to play even in the highly programmatic en- vironment of the Manhattan Project. Not surprisingly this mode of opera- tion evolved into the remarkable and unique admixture of pure, applied, programmatic, and technological re- search that is the hallmark of the present Laboratory structure. No- where in the world today can one find under one roof such diversity of talent dealing with such a broad range of scientific and technological challenges—from questions con- cerning the evolution of the universe and the nature of elementary parti- cles to the structure of new materi- als, the design and control of weapons, the mysteries of the gene, and the nature of AIDS! Many of the original scientists would have, in today’s parlance, identified themselves as nuclear or particle physicists. They explored the most basic laws of physics and continued the search for and under- standing of the “fundamental build- ing blocks of nature’’ and the princi- t is a well-known, and much- grappled with deep questions con- ples that govern their interactions. overworked, adage that the group cerning the consequences of quan- It is therefore fitting that this area of Iof scientists brought to Los tum mechanics, the structure of the science has remained a highly visi- Alamos to work on the Manhattan atom and its nucleus, and the devel- ble and active component of the Project constituted the greatest as- opment of quantum electrodynamics basic research activity at Los Alam- semblage of scientific talent ever (QED, the relativistic quantum field os. -
Gravity, Inertia, and Quantum Vacuum Zero Point Fields
Foundations of Physics, Vol.31,No. 5, 2001 Gravity, Inertia, and Quantum Vacuum Zero Point Fields James F. Woodward1 Received July 27, 2000 Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electri- cally charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reac- tion forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. 1. INTRODUCTION Several years ago Haisch, Rueda, and Puthoff (1) (hereafter, HRP) pub- lished a lengthy paper in which they claimed that a substantial part, indeed perhaps all of normal inertial reaction forces could be understood as the action of the electromagnetic zero-point field (EZPF), expected on the basis of quantum field theory, on electric charges of normal matter. In several subsequent papers Haisch and Rueda particularly have pressed this claim, making various modifications to the fundamental argument to try to deflect several criticisms. -
Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical. -
Quantum Vacuum Energy Density and Unifying Perspectives Between Gravity and Quantum Behaviour of Matter
Annales de la Fondation Louis de Broglie, Volume 42, numéro 2, 2017 251 Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter Davide Fiscalettia, Amrit Sorlib aSpaceLife Institute, S. Lorenzo in Campo (PU), Italy corresponding author, email: [email protected] bSpaceLife Institute, S. Lorenzo in Campo (PU), Italy Foundations of Physics Institute, Idrija, Slovenia email: [email protected] ABSTRACT. A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. This model introduces the possibility to interpret gravity and the quantum behaviour of matter as two different aspects of the same origin. The change of the quantum vacuum energy density can be considered as the fundamental medium which determines a bridge between gravity and the quantum behaviour, leading to new interest- ing perspectives about the problem of unifying gravity with quantum theory. PACS numbers: 04. ; 04.20-q ; 04.50.Kd ; 04.60.-m. Key words: general relativity, three-dimensional space, quantum vac- uum energy density, quantum mechanics, generalized Klein-Gordon equation for the quantum vacuum energy density, generalized Dirac equation for the quantum vacuum energy density. 1 Introduction The standard interpretation of phenomena in gravitational fields is in terms of a fundamentally curved space-time. However, this approach leads to well known problems if one aims to find a unifying picture which takes into account some basic aspects of the quantum theory. For this reason, several authors advocated different ways in order to treat gravitational interaction, in which the space-time manifold can be considered as an emergence of the deepest processes situated at the fundamental level of quantum gravity. -
Aspects of Loop Quantum Gravity
Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models . -
A Note on Conformally Compactified Connection Dynamics Tailored For
A note on conformally compactified connection dynamics tailored for anti-de Sitter space N. Bodendorfer∗ Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland October 9, 2018 Abstract A framework conceptually based on the conformal techniques employed to study the struc- ture of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions. 1 Introduction The study of asymptotic conditions on spacetimes has received wide interest within general relativity. Most notably, the concept of asymptotic flatness can serve as a model for isolated systems and one can, e.g., study a system’s total energy or the amount of gravitational ra- diation emitted [1]. More recently, with the discovery of the AdS/CFT correspondence [2], asymptotically anti de Sitter spacetimes have become a focus of interest. In a certain low en- ergy limit of the correspondence, computations on the gravitational side correspond to solving the Einstein equations with anti-de Sitter asymptotics. Within loop quantum gravity (LQG), the issue of non-compact spatial slices or asymptotic conditions on spacetimes has received only little attention so far due to a number of technical reasons. However, also given the recent interest in holography from a loop quantum gravity point of view [3, 4, 5], this question is important to address. -
Open Dissertation-Final.Pdf
The Pennsylvania State University The Graduate School The Eberly College of Science CORRELATIONS IN QUANTUM GRAVITY AND COSMOLOGY A Dissertation in Physics by Bekir Baytas © 2018 Bekir Baytas Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2018 The dissertation of Bekir Baytas was reviewed and approved∗ by the following: Sarah Shandera Assistant Professor of Physics Dissertation Advisor, Chair of Committee Eugenio Bianchi Assistant Professor of Physics Martin Bojowald Professor of Physics Donghui Jeong Assistant Professor of Astronomy and Astrophysics Nitin Samarth Professor of Physics Head of the Department of Physics ∗Signatures are on file in the Graduate School. ii Abstract We study what kind of implications and inferences one can deduce by studying correlations which are realized in various physical systems. In particular, this thesis focuses on specific correlations in systems that are considered in quantum gravity (loop quantum gravity) and cosmology. In loop quantum gravity, a spin-network basis state, nodes of the graph describe un-entangled quantum regions of space, quantum polyhedra. We introduce Bell- network states and study correlations of quantum polyhedra in a dipole, a pentagram and a generic graph. We find that vector geometries, structures with neighboring polyhedra having adjacent faces glued back-to-back, arise from Bell-network states. The results present show clearly the role that entanglement plays in the gluing of neighboring quantum regions of space. We introduce a discrete quantum spin system in which canonical effective methods for background independent theories of quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building- up and stability of long-range correlations.