DOCSLIB.ORG

Aspects of Lorentz and CPT Violation in Cosmology

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Aspects of Lorentz and CPT Violation in Cosmology NATIONAL CENTRE FOR NUCLEAR RESEARCH DOCTORAL THESIS Aspects of Lorentz and CPT Violation in Cosmology Author: Supervisor: Nils Albin NILSSON Prof. Dr Hab. Mariusz P. DA¸BROWSKI A thesis submitted in fulfillment of the requirements for the degree of Doctor of Physical Sciences at the National Centre for Nuclear Research March 10, 2020 iii Declaration of Authorship I, Nils Albin NILSSON, declare that this thesis titled, “Aspects of Lorentz and CPT Violation in Cosmology” and the work presented in it are my own. I confirm that: • This work was done wholly or mainly while in candidature for a research de- gree at the National Centre for Nuclear Research. • Where any part of this thesis has previously been submitted for a degree or any other qualification at the National Centre for Nuclear Research or any other institution, this has been clearly stated. • Where I have consulted the published work of others, this is always clearly attributed. • Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. • I have acknowledged all main sources of help. • Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed my- self. Signed: Date: v “Nature never deceives us; it is always we who deceive ourselves” Jean-Jaques Rousseau vii NATIONAL CENTRE FOR NUCLEAR RESEARCH Abstract National Centre for Nuclear Research Doctor of Physical Sciences Aspects of Lorentz and CPT Violation in Cosmology by Nils Albin NILSSON The breaking of Lorentz symmetry can give rise to a wealth of observational con- sequences. The main topic of this thesis is to explore models of gravitation and cosmology with Lorentz symmetry violation (closely linked to Charge-Parity-Time (CPT) violation). Five Lorentz-violating models or frameworks are outlined in this thesis, and three of these are subsequently chosen and studied in the following chap- ters. Doubly General Relativity breaks Lorentz symmetry through a modification of the dispersion relation of particles. This is combined with the kinematic modified dispersion relations common in phenomenological studies of Lorentz violation with high-energy gamma rays. By applying a large cosmological dataset to the result- ing model, it is found that the lower limit on the energy scale of Lorentz violation is 16 ELV ∼ 10 GeV (1s). Hoˇrava-Lifshitzgravity is a possibly UV-complete quantum- gravity theory candidate. By again applying a large updated cosmological dataset new constraints on the cosmological parameters are found. In particular, the curva- −3 ture density parameter Wk found to be non-zero (−3.30 ± 0.20) × 10 (1s). More- over, this model is discussed in context of the Hubble parameter tension, through which the Hoˇrava-Lifshitzcoupling parameter lis given new contraints. It is found that Lorentz violation can contribute up to 38% of the Hubble tension. The Standard- Model Extension is a general, theory-agnostic framework for testing Lorentz and CPT violation. Here, the Hamiltonian formulation of the Standard-Model Extension gravitational sector is presented. viii Polski: Łamanie symetrii Lorentza moze˙ prowadzi´cdo wielu konsekwencji obserwacyjnych. Głównym tematem rozprawy jest zbadanie modeli grawitacyjnych i kosmologicznych, w których zachodzi scenariusz naruszenia tej symetrii (blisko spokrewnione ze zła- maniem symetrii CPT – Ładunku, Parzysto´sci,Czasu). W pracy opisano pi˛e´cróznych˙ modeli ze scenariuszem łamania symetrii Lorentza, z czego trzy s ˛awybrane do dal- szej analizy w kolejnych rozdziałach. Podwójna Ogólna Teoria Wzgl˛edno´sci(Dou- bly General Relativity) łamie symetri˛eLorentza poprzez modyfikacj˛erelacji dysper- syjnych cz ˛astek.Powyzszy˙ model jest poł ˛aczonyz kinematycznie zmodyfikowanymi relacjami dyspersyjnymi powszechnymi w badaniach fenomenologicznych łamania symetrii Lorentza za pomoc ˛awysokoenergetycznych promieni gamma. Porównu- j ˛acuzyskany model z szerokim zestawem danych kosmologicznych stwierdzono, 16 ze˙ dolna granica skali energii łami ˛acejsymetri˛eLorentza wynosi ELV ∼ 10 GeV (1s). Teoria grawitacji Hoˇravy-Lifszyca jest potencjalnym kandydatem na kom- pletn ˛aw ultrafiolecie teori˛ekwantowej grawitacji. Ponownie, poprzez zastosowanie wielkich zestawów danych kosmologicznych do tego modelu, udało si˛ewyznaczy´c nowe ograniczenia na warto´scijego parametrów kosmologicznych. W szczegól- no´scistwierdzono, ze˙ krzywizna przestrzeni jest niezerowa (−3, 30 ± 0, 20) × 10−3 (1s). Co wi˛ecej,model ten jest omawiany w kontek´scierozbiezno´scidotycz˙ ˛acych parametru Hubble’a (Hubble parameter tension), w wyniku czego otrzymuje si˛e nowe ograniczenia na warto´s´cparametru l w teorii Hoˇravy-Lifszyca.Stwierdzono, ze˙ scenariusz łamania symetrii Lorentza moze˙ przyczyni´csi˛ew 38% do rozwi ˛aza- nia problemu rozbiezno´sciparametru˙ Hubble’a. Rozszerzony Model Standardowy jest ogóln ˛a,efektywn ˛ateori ˛apola mog ˛ac˛aposłuzy´cdo˙ testowania scenariuszy ła- mania symetrii Lorentza. W rozprawie, zaprezentowane jest Hamiltonowskie sfor- mułowanie sektora grawitacyjnego dla Rozszerzonego Modelu Standardowego. ix Svenska: Lorentzbrott kan ge upphov till mängder av observerbara konsekvenser. Denna avhandlings huvudtema är att utforska gravitations- och kosmologimodeller som inkluderar Lorentzbrott (kopplat till Laddning-Paritet-Tidbrott (CPT)). Fem Lorentzbry- tande modeller och ramverk skissas i början av denna avhandling och tre av dessa väljs sedermera ut och studeras i efterföljande kapitel. Dubbelt Allmän Relativitet- steori (Doubly General Relativity) bryter Lorentzsymmetri genom att modifiera dis- persionsrelationen för partiklar. Detta kombineras med de kinematiskt modifierade dispersionsrelationerna som är vanliga i fenomenologiska studier av högenergifo- toner. Genom att applicera ett stort kosmologiskt dataset på den resulterande kos- mologiska modellen bestämdes det lägre värdet för den karakteristiska energiskalan 16 för Lorentzbrott till ELV ∼ 10 GeV (1s). Hoˇrava-Lifshitzgravitationär en möjli- gen UV-komplett kvantgravitationskandidat. Genom att återigen applicera ett stort uppdaterat kosmologiskt dataset bestäms nya värden på de kosmologiska parame- trarna. I synnerhet kan den spatiala kurvaturen bestämmas till (−3.30 ± 0.20) × 10−3 (1s). Hubblespänningen (Hubble tension) diskuteras också inom denna mod- ell som en effekt av föredragna referensramar (preferred-frame effects), och värden på Hoˇrava-Lifshitzparametrarbestäms från Hubblespänningsdata. Det fastställs också att Lorentzbrott kan bidra med upp till 38% av Hubblespänningen. Stan- dardmodellutvidgningen (Standard-Model Extension) är ett allmännt ramverk för att parametrisera och testa Lorentz- och CPT-brott. Här härleds och presenteras Hamiltonformuleringen av Standardmodellutvidgningens gravitationssektor. xi Acknowledgements The writing of this thesis would not have been possible without the support and guidance of my supervisor, Mariusz P. Da¸browski, who gave me a lot of research freedom and encouraged me to be independent. His influence has made me the researcher who I am today and has helped shape this thesis into what is printed within these pages. To Ewa Czuchry, who took me in when all I had was an idea and encouraged me to tackle hard problems. To Vincenzo Salzano who taught me about MCMC and patiently answered my endless questions. To Quentin Bailey and Kellie O’Neal-Ault who helped open the door to an exciting field and for helping me develop a long-term collaboration, and to all the people at Embry-Riddle for treating me like one of their own from day one. To Artur and Viktor, with whom I could always discuss ideas, and to Harrison for proofreading parts of this thesis. To my parents, who supported me even when it brought me far from home, and to Sarah, for her unwaivering support. Special thanks goes to the National Centre for Nuclear Research and National Science Center. Their financial support made it possible for me to attend confer- ences and visit scientists in Poland, Germany, Italy, Greece, Portugal, Canada, and the USA. I also thank the National Centre for Nuclear Research for the use of the CIS´ high-performance computing cluster. To all the people who have helped me along the way, thank you. xiii Contents Declaration of Authorship iii Abstract vii Acknowledgements xi 1 Introduction1 1.1 Research Aims and Scope..........................5 1.2 Linkage of Scientific Papers.........................6 2 The Role of Lorentz and CPT Symmetry in Modern Physics7 2.1 Explicit versus Spontaneous Lorentz Symmetry Breaking........8 2.2 CPT Symmetry in an Expanding Universe................. 10 2.3 General Properties of Models with Lorentz Violation........... 11 2.4 Common Lorentz-Violating Models and Frameworks.......... 12 2.4.1 Doubly General Relativity...................... 12 2.4.2 Hoˇrava-LifshitzGravity....................... 15 2.4.3 Einstein-Aether Theory....................... 17 2.4.4 Bumblebee Gravity.......................... 18 2.4.5 The Standard-Model Extension................... 20 3 Modified Dispersion Relations in Gravity; Doubly General Relativity 23 3.1 Lorentz Invariance Violation in Rainbow Gravity............. 25 3.1.1 Lorentz Invariance Violation.................... 25 3.1.2 Simple Lorentz Invariance Violating Cosmological Framework 26 3.1.3 Two specific choices of the scaling function h±(E) ........ 29 3.1.4 Comparison with the LCDM model................ 30 3.2 Discussion and Conclusions......................... 32 xiv
Load more

Recommended publications
  • Methods for Cancellation of Apparent Cerenkov Radiation Arising From
    University of South Carolina Scholar Commons Theses and Dissertations Summer 2020 Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates Richard Henry DeCosta Follow this and additional works at: https://scholarcommons.sc.edu/etd Part of the Physics Commons Recommended Citation DeCosta, R. H.(2020). Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/6003 This Open Access Dissertation is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Methods For Cancellation Of Apparent Cerenkov Radiation Arising From SME Models And Separability Of Schrödinger’s Equation Using Exotic Potentials In Parabolic Coordinates by Richard Henry DeCosta Associate of Arts Clinton Community College Bachelor of Arts Plattsburgh State University Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics College of Arts and Sciences University of South Carolina 2020 Accepted by: Brett Altschul, Major Professor Matthias Schindler, Committee Member Scott Crittenden, Committee Member Daniel Dix, Committee Member Cheryl L. Addy, Vice Provost and Dean of the Graduate School © Copyright by Richard Henry DeCosta, 2020 All Rights Reserved. ii Abstract In an attempt to merge the two prominent areas of physics: The Standard Model and General Relativity, there have been many theories for the underlying physics that may lead to Lorentz- and CPT-symmetry violations.
    [Show full text]
  • Einstein's Wrong
    Einstein’s wrong way: from STR to GTR Adrian Ferent I discovered a new Gravitation theory which breaks the wall of Planck scale! Abstract My Nobel Prize - Discoveries “Starting from STR, it is not possible to find a Quantum Gravity theory” Adrian Ferent “Einstein was on the wrong way: from STR to GTR” Adrian Ferent “Starting from STR, Einstein was not able to explain Gravitation” Adrian Ferent “Starting from STR, Einstein was not able to explain Gravitation, he calculated Gravitation” Adrian Ferent “Einstein's equivalence principle is wrong because the gravitational force experienced locally is caused by a negative energy, gravitons energy and the force experienced by an observer in a non-inertial (accelerated) frame of reference is caused by a positive energy.” Adrian Ferent “Because Einstein's equivalence principle is wrong, Einstein’s gravitation theory is wrong.” Adrian Ferent “Because Einstein’s gravitation theory is wrong, LQG, String theory… are wrong theories” Adrian Ferent “Einstein bent the space, Ferent unbent the space” Adrian Ferent 1 “Einstein bent the time, Ferent unbent the time” Adrian Ferent “I am the first who Quantized the Gravitational Field!” Adrian Ferent “I quantized the gravitational field with gravitons” Adrian Ferent “Gravitational field is a discrete function” Adrian Ferent “Gravitational waves are carried by gravitons” Adrian Ferent In STR and GTR there are continuous functions. This is another proof that LIGO is a fraud. The 2017 Nobel Prize in Physics has been awarded for a project, the Laser Interferometer Gravitational-wave Observatory (LIGO) not for a scientific discovery; they did not detect anything because Einstein’s gravitational waves do not exist.
    [Show full text]
  • Neutrino Oscillations in the Early Universe with Nonequilibrium Neutrino Distributions
    PHYSICAL REVIE% D VOLUME 52, NUMBER 6 15 SEPTEMBER 1995 Neutrino oscillations in the early Universe with nonequilibrium neutrino distributions V. Alan Kostelecky Physics Department, Indiana University, Bloomington, Indiana $7405 Stuart Samuel* Maz Plan-ck Inst-itut fur Physik, Werner Heis-enberg Insti-tut, Fohringer Ring 8, 80805 Munich, Germany (Received 28 March 1995) Around one second after the big bang, neutrino decoupling and e+-e annihilation distorted the Fermi-Dirac spectrum of neutrino energies. Assuming neutrinos have masses and can mix, we compute the distortions using nonequilibrium thermodynamics and the Boltzmann equation. The Bavor behavior of neutrinos is studied during and following the generation of the distortion. PACS number(s): 95.30.Cq, 12.15.Ff, 14.60.Pq I. INTRODUCTION cause the neutrinos are decoupling at this time. Due to W+ exchanges, electron neutrinos are heated some- what more than and w neutrinos. This leads to an Neutrinos play a significant role both in cosmology [1] p excess of electron neutrinos over and w neutrinos. Fur- and in particle physics [2]. In cosmology, during the p, radiation-dominated period in the early Universe from thermore, higher-energy neutrinos interact more strongly one second after the big bang to around twenty-thousand than lower-energy neutrinos so that a relative excess of neutrinos arises. years, neutrinos are almost as important as photons in higher-energy The appearance of a fa- driving the expansion of the Universe. Furthermore, nu- vor excess means that neutrino oscillations can occur. cleosynthesis and the ensuing abundances of light ele- This potentially could afFect nucleosynthesis [5].
    [Show full text]
  • Neutrino Cosmology and Large Scale Structure
    Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 Neutrino cosmology and large scale structure Christiane Stefanie Lorenz Pembroke College and Sub-Department of Astrophysics University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity 2019 The topic of this thesis is neutrino cosmology and large scale structure. First, we introduce the concepts needed for the presentation in the following chapters. We describe the role that neutrinos play in particle physics and cosmology, and the current status of the field. We also explain the cosmological observations that are commonly used to measure properties of neutrino particles. Next, we present studies of the model-dependence of cosmological neutrino mass constraints. In particular, we focus on two phenomenological parameterisations of time-varying dark energy (early dark energy and barotropic dark energy) that can exhibit degeneracies with the cosmic neutrino background over extended periods of cosmic time. We show how the combination of multiple probes across cosmic time can help to distinguish between the two components. Moreover, we discuss how neutrino mass constraints can change when neutrino masses are generated late in the Universe, and how current tensions between low- and high-redshift cosmological data might be affected from this. Then we discuss whether lensing magnification and other relativistic effects that affect the galaxy distribution contain additional information about dark energy and neutrino parameters, and how much parameter constraints can be biased when these effects are neglected.
    [Show full text]
  • Nobel Lecture: Accelerating Expansion of the Universe Through Observations of Distant Supernovae*
    REVIEWS OF MODERN PHYSICS, VOLUME 84, JULY–SEPTEMBER 2012 Nobel Lecture: Accelerating expansion of the Universe through observations of distant supernovae* Brian P. Schmidt (published 13 August 2012) DOI: 10.1103/RevModPhys.84.1151 This is not just a narrative of my own scientific journey, but constant, and suggested that Hubble’s data and Slipher’s also my view of the journey made by cosmology over the data supported this conclusion (Lemaˆitre, 1927). His work, course of the 20th century that has lead to the discovery of the published in a Belgium journal, was not initially widely read, accelerating Universe. It is complete from the perspective of but it did not escape the attention of Einstein who saw the the activities and history that affected me, but I have not tried work at a conference in 1927, and commented to Lemaˆitre, to make it an unbiased account of activities that occurred ‘‘Your calculations are correct, but your grasp of physics is around the world. abominable.’’ (Gaither and Cavazos-Gaither, 2008). 20th Century Cosmological Models: In 1907 Einstein had In 1928, Robertson, at Caltech (just down the road from what he called the ‘‘wonderful thought’’ that inertial accel- Edwin Hubble’s office at the Carnegie Observatories), pre- eration and gravitational acceleration were equivalent. It took dicted the Hubble law, and claimed to see it when he com- Einstein more than 8 years to bring this thought to its fruition, pared Slipher’s redshift versus Hubble’s galaxy brightness his theory of general Relativity (Norton and Norton, 1984)in measurements, but this observation was not substantiated November, 1915.
    [Show full text]
  • CPT Violation and the Standard Model
    PHYSICAL REVIEW D VOLUME 55, NUMBER 11 1 JUNE 1997 CPT violation and the standard model Don Colladay and V. Alan Kostelecky´ Department of Physics, Indiana University, Bloomington, Indiana 47405 ~Received 22 January 1997! Spontaneous CPT breaking arising in string theory has been suggested as a possible observable experimen- tal signature in neutral-meson systems. We provide a theoretical framework for the treatment of low-energy effects of spontaneous CPT violation and the attendant partial Lorentz breaking. The analysis is within the context of conventional relativistic quantum mechanics and quantum field theory in four dimensions. We use the framework to develop a CPT-violating extension to the minimal standard model that could serve as a basis for establishing quantitative CPT bounds. @S0556-2821~97!05211-9# PACS number~s!: 11.30.Er, 11.25.2w, 12.60.2i I. INTRODUCTION a general methodology that is compatible with desirable fea- tures like microscopic causality while being sufficiently de- Among the symmetries of the minimal standard model is tailed to permit explicit calculations. invariance under CPT. Indeed, CPT invariance holds under We suppose that underlying the effective four- mild technical assumptions for any local relativistic point- dimensional action is a complete fundamental theory that is particle field theory @1–5#. Numerous experiments have con- based on conventional quantum physics @15# and is dynami- firmed this result @6#, including in particular high-precision cally CPT and Poincare´ invariant. The fundamental theory is tests using neutral-kaon interferometry @7,8#. The simulta- assumed to undergo spontaneous CPT and Lorentz breaking. neous existence of a general theoretical proof of CPT invari- In a Poincare´-observer frame in the low-energy effective ac- ance in particle physics and accurate experimental tests tion, this process is taken to fix the form of any CPT- and makes CPT violation an attractive candidate signature for Lorentz-violating terms.
    [Show full text]
  • Topics in Particle Physics and Cosmology Beyond the Standard
    Topics in Theoretical Particle Physics and Cosmology Beyond the Standard Model Thesis by Alejandro Jenkins In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy arXiv:hep-th/0607239v1 29 Jul 2006 California Institute of Technology Pasadena, California 2008 (Defended 26 May, 2006) ii c 2008 Alejandro Jenkins All Rights Reserved iii Para Viviana, quien, sin nada de esto, hubiera sido posible (sic) iv If I have not seen as far as others, it is because giants were standing on my shoulders. — Prof. Hal Abelson, MIT v Acknowledgments How small the cosmos (a kangaroo’s pouch would hold it), how paltry and puny in comparison to human consciousness, to a single individual recollection, and its expression in words! — Vladimir V. Nabokov, Speak, Memory What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent? — Richard P. Feynman, “The Relation of Physics to Other Sciences” I thank Mark Wise, my advisor, for teaching me quantum field theory, as well as a great deal about physics in general and about the professional practice of theoretical physics. I have been honored to have been Mark’s student and collaborator, and I only regret that, on account of my own limitations, I don’t have more to show for it. I thank him also for many free dinners with the Monday seminar speakers, for his patience, and for his sense of humor. I thank Steve Hsu, my collaborator, who, during his visit to Caltech in 2004, took me under his wing and from whom I learned much cosmology (and with whom I had interesting conversations about both the physics and the business worlds).
    [Show full text]
  • Instructions to Authors
    www.elsevier.com/locate/physletb Instructions to authors Aims and Scope Physics Letters B ensures the rapid publication of letter-type communications in the fields of Nuclear Physics, Particle Physics and Astrophysics. Articles should influence the physics community significantly. Submission Electronic submission is strongly encouraged. The electronic file, accompanied by a covering message, should be e-mailed to one of the Editors indicated below. If electronic submission is not feasible, submission in print is possible, but it will delay publication. In the latter case manuscripts (one original + two copies), accompanied by a covering letter, should be sent to one of the following Editors: L. Alvarez-Gaumé, Theory Division, CERN, CH-1211 Geneva 23, Switzerland, E-mail address: Luis.Alvarez-Gaume@CERN. CH Theoretical High Energy Physics (General Theory) J.-P. Blaizot, ECT*, Strada delle Tabarelle, 266, I-38050 Villazzano (Trento), Italy, E-mail address: [email protected]. FR Theoretical Nuclear Physics M. Cvetic,ˇ David Rittenhouse Laboratory, Department of Physics, University of Pennsylvania, 209 S, 33rd Street, Philadelphia, PA 19104-6396, USA, E-mail address: [email protected] Theoretical High Energy Physics M. Doser, EP Division, CERN, CH-1211 Geneva 23, Switzerland, E-mail address: [email protected] Experimental High Energy Physics D.F. Geesaman, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA, E-mail address: [email protected] Experimental Nuclear Physics H. Georgi, Department of Physics, Harvard University, Cambridge, MA 02138, USA, E-mail address: Georgi@PHYSICS. HARVARD.EDU Theoretical High Energy Physics G.F. Giudice, CERN, CH-1211 Geneva 23, Switzerland, E-mail address: [email protected] Theoretical High Energy Physics N.
    [Show full text]
  • CPT Theorem and Classification of Topological Insulators And
    CPT theorem and classification of topological insulators and superconductors Chang-Tse Hsieh,1 Takahiro Morimoto,2 and Shinsei Ryu1 1Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St, Urbana IL 61801 2Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama, 351-0198, Japan (ΩDated: June 3, 2014) We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification of gapped quadratic fermion theories with symmetries, and the other in terms of the K-matrix theory description of the edge theory of (2+1)-dimensional bulk theories. The first approach is specific to free fermion theories in general spatial dimensions while the second approach is limited to two spatial dimensions but incorporates effects of interactions. We also clarify the role of CPT theorem in classification of symmetry-protected topological phases, and show, in particular, topological superconductors dis- cussed before are related by CPT theorem. CONTENTS VI. Discussion 19 I. Introduction 1 Acknowledgments 19 A. Outline and main results 3 A. Entanglement spectrum and effective symmetries 19 II. 2D fermionic topological phases protected by 1.Entanglementspectrum 20 symmetries 4 2. Properties of entanglement spectrum with A. CP symmetric insulators 4 symmetries 21 1. tight-binding model 4 2.Edgetheory 5 B. Calculations of symmetry transformations and B. BdG systems with spin U(1) and P SPT phases in K-matrix theories 21 symmetries 5 1. Algebraic relations of symmetry operators 21 C. Connection to T symmetric insulators 6 2.
    [Show full text]
  • Spontaneous Lorentz Violation, Nambu-Goldstone Modes, And
    SPONTANEOUS LORENTZ VIOLATION, NAMBU-GOLDSTONE MODES, AND MASSIVE MODES ROBERT BLUHM Department of Physics and Astronomy, Colby College Waterville, ME 04901, USA In any theory with spontaneous symmetry breaking, it is important to account for the massless Nambu-Goldstone and massive Higgs modes. In this short review, the fate of these modes is examined for the case of a bumblebee model, in which Lorentz symmetry is spontaneously broken. 1 Spontaneous Lorentz violation Spontaneous symmetry breaking has three well-known consequences. The first is Goldstone’s theorem, which states that massless Nambu-Goldstone (NG) modes should appear when a continuous symmetry is spontaneously broken. The second is that massive Higgs modes can appear, consisting of excitations out of the degenerate minimum. The third is the Higgs mechanism, which can occur when the broken symmetry is local. In conventional particle physics, these processes involve a scalar field with a nonzero vacuum expectation value that induces spontaneous breaking of gauge symmetry. However, in this paper, these processes are examined for the case where it is a vector field that has a nonzero vacuum value and where the symmetry that is spontaneously broken is Lorentz symmetry. The idea of spontaneous Lorentz violation is important in quantum-gravity theory. For example, in string field theory, mechanisms have been found that can lead to spontaneous Lorentz violation.1 It has also been shown that sponta- neous Lorentz breaking is compatible with geometrical consistency conditions 2 arXiv:1008.1805v1 [hep-th] 10 Aug 2010 in gravity, while explicit Lorentz breaking is not. The Standard-Model Extension (SME) describes Lorentz-violating inter- actions at the level of effective field theory.
    [Show full text]
  • CPT, Lorentz Invariance, Mass Differences, and Charge Non
    CPT, Lorentz invariance, mass differences, and charge non-conservation A.D. Dolgova,b,c,d, V.A. Novikova,b September 11, 2018 a Novosibirsk State University, Novosibirsk, 630090, Russia b Institute of Theoretical and Experimental Physics, Moscow, 113259, Russia cDipartimento di Fisica, Universit`adegli Studi di Ferrara, I-44100 Ferrara, Italy dIstituto Nazionale di Fisica Nucleare, Sezione di Ferrara, I-44100 Ferrara, Italy Abstract A non-local field theory which breaks discrete symmetries, including C, P, CP, and CPT, but preserves Lorentz symmetry, is presented. We demonstrate that at one-loop level the masses for particle and antiparticle remain equal due to Lorentz symmetry only. An inequality of masses implies breaking of the Lorentz invariance and non-conservation of the usually conserved charges. arXiv:1204.5612v1 [hep-ph] 25 Apr 2012 1 1 Introduction The interplay of Lorentz symmetry and CPT symmetry was considered in the literature for decades. The issue attracted an additional interest recently due to a CPT-violating sce- nario in neutrino physics with different mass spectrum of neutrinos and antineutrinos [1]. Theoretical frameworks of CPT breaking in quantum field theories, in fact in string theo- ries, and detailed phenomenology of oscillating neutrinos with different masses of ν andν ¯ was further studied in papers [2]. On the other hand, it was argued in ref. [3] that violation of CPT automatically leads to violation of the Lorentz symmetry [3]. This might allow for some more freedom in phenomenology of neutrino oscillations. Very recently this conclusion was revisited in our paper [4]. We demonstrated that field theories with different masses for particle and antiparticle are extremely pathological ones and can’t be treated as healthy quantum field theories.
    [Show full text]
  • Issues in Physics & Astronomy
    Issues in Physics & Astronomy Board on Physics and Astronomy · The National Academies · Washington, D.C. · 202-334-3520 · national-academies.org/bpa · Summer 2009 Challenges and Opportunities in New Materials Synthesis and Crystal Growth James C. Lancaster, BPA Staff or much of the past 60 years, the Madison), was charged with the respon- ficiently interesting scientifically or relevant U.S. research community dominat- sibility of assessing the health of research for an application—or as often happens, Fed the discovery of new crystalline activities in the United States in this field, both—large single crystals of that material materials and the growth of large single identifying future opportunities and rec- are needed for detailed study. Because of crystals. These efforts placed the country at ommending strategies for the United States common heritage, shared resources, and the forefront of fundamental advances in to reinvigorate its efforts and thereby return strong educational bonds, it is natural to condensed-matter sciences and fueled the to a position of leadership in this field. The combine these related activities—the dis- development of many of the new technolo- committee issued its report this past spring. covery and growth of crystalline materials gies at the core of U.S. economic growth. The two activities in this field— (DGCM)—in a single study. The growth of The opportunities offered by future devel- discovering new crystalline materials and thin, two-dimensional crystalline films also opments in this field remain as promising growing large crystals of these materials— is included in this study because it shares as the achievements of the past.
    [Show full text]