DOCSLIB.ORG

Sum Rules on Quantum Hadrodynamics at Finite Temperature

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Sum Rules on Quantum Hadrodynamics at Finite Temperature Sum rules on quantum hadrodynamics at finite temperature and density B. X. Sun1∗, X. F. Lu2;3;7, L. Li4, P. Z. Ning2;4, P. N. Shen7;1;2, E. G. Zhao2;5;6;7 1Institute of High Energy Physics, The Chinese Academy of Sciences, P.O.Box 918(4), Beijing 100039, China 2Institute of Theoretical Physics, The Chinese Academy of Sciences, Beijing 100080, China 3Department of Physics, Sichuan University, Chengdu 610064, China 4Department of Physics, Nankai University, Tianjin 300071, China 5Center of Theoretical Nuclear Physics, National Laboratory of Heavy ion Accelerator,Lanzhou 730000, China 6Department of Physics, Tsinghua University, Beijing 100084, China 7China Center of Advanced Science and Technology(World Laboratory), Beijing 100080,China October 15, 2003 Abstract According to Wick's theorem, the second order self-energy corrections of hadrons in the hot and dense nuclear matter are calculated. Furthermore, the Feynman rules ∗Corresponding author. E-mail address: [email protected]. Present address: Laboratoire de Physique Subatomique et de Cosmologie, IN2P3/CNRS, 53 Av. des Martyrs, 38026 Grenoble-cedex, France 1 are summarized, and the method of sum rules on quantum hadrodynamics at finite temperature and density is developed. As the strong couplings between nucleons are considered, the self-consistency of this method is discussed in the framework of relativistic mean-field approximation. Debye screening masses of the scalar and vector mesons in the hot and dense nuclear matter are calculated with this method in the relativistic mean-field approximation. The results are different from those of thermofield dynamics and Brown-Rho conjecture. Moreover, the effective masses of the photon and the nucleon in the hot and dense nuclear matter are discussed. PACS numbers : 21.65.+f, 24.10.Cn, 24.10.Jv, 24.10.Pa 2 1 Introduction The quantum field theory, introduced to solve the many-body problems since the late fifties, has proved to be highly successful in studying the ground state, the equilibrium and non-equilibrium properties at finite temperature[1, 2, 3, 4, 5, 6, 7, 8, 9]. These theories to solve many-body problems are based on the conjecture that all of the effects of the medium at finite temperature and density would change the propagators of particles. When the propagators in the mediums are obtained, the properties of particles and the equation of state of the medium can be calculated easily. The propagators of particles in the medium are different from those in vacuum correspondingly, so this conjecture means the redefinition of the "vacuum", and the calculation procedures are all carried out in this new "vacuum". In a series of our previous papers[10, 11, 12], according to Wick's theorem, we have developed a new method, sum rules on quantum hadrodynamics to solve the nuclear many-body problems. In this method, the Feynman propagators in vacuum are adopted, and the second order self-energies of particles in the nuclear matter are calculated, while the effects of the nuclear matter are treated as the condensations of nucleons and mesons. It shows the same results as the method of quantum hadrodynamics[1, 2, 3]. With this new method, we have studied the effective masses of the photon and mesons[10, 11], and constructed the density-dependent relativistic mean-field model[11]. In this paper we will generalize this new method to the situation at finite temperature and density. The organization of this paper is as follows. The second order self-energy corrections of the nucleon and the meson in nuclear matter are calculated from Wick expansion in the framework of quantum hadrodynamics 1 in Sec. 2, then the Feynman rules and self- consistency for this method at finite temperature and density are summarized in Sec. 3. The results of screening masses of mesons are presented in Sec. 4. In Sec. 5, the effective mass of the photon in the hot nuclear matter is discussed. The summary is given in Sec. 6. 3 2 The self-energies of hadrons in the hot and dense nuclear matter According to Walecka-1 model, the Lagrangian density in nuclear matter can be written as 1 1 1 1 L = ¯ (iγ @µ − M ) + @ σ@µσ − m2 σ2 − ! !µν + m2 ! !µ µ N 2 µ 2 σ 4 µν 2 ! µ µ −gσ ¯σ − g! ¯γµ! ; (1) where is the field of the nucleon, MN is the nucleon mass, and !µν = @µ!ν − @ν!µ; (2) is the field tensor of the vector meson. In the hot nuclear matter, the expectations of normal products of the creation opera- tor and corresponding annihilation operator are relevant to the distribution functions of particles. y 3 ~0 0 h N; β jAp0λ0 Apλj N; β i = nF δ (p − p~)δλ λ; (3) y 3 ~0 0 h N; β jBp0λ0 Bpλj N; β i = n¯F δ (p − p~)δλ λ; (4) 0 where λ and λ denote spins of fermions, nF and n¯F are the distribution functions of the nucleon and antinucleon, respectively. 1 n = ; (5) F exp [(E(p) − µ)=T ] + 1 1 n¯ = ; (6) F exp [(E(p) + µ)=T ] + 1 2 2 where E(p) = p~ + MN , and µ is the chemical potential of the nucleon. The relation q of chemical potential and the number density of nucleons ρB is 2 3 ρB = 3 d p [nF − n¯F ] : (7) (2π) Z 4 y 3 ~0 ~ h N; β jak0 akj N; β i = nσδ (k − k); (8) y 3 ~0 ~ 0 h N; β jbk0δ0 bkδj N; β i = n!δ (k − k)δδ δ; (9) 0 where δ and δ denote the spins of the vector meson, nσ and n! are the boson distribution functions of the scalar and vector mesons, respectively. 1 nα = ; α = σ; !; (10) exp [jΩαj=T − 1] ~ 2 2 where Ωα = k + mα. Since the meson number is not conserved in nuclear matter, there q is not the contribution of the meson chemical potential in the boson distribution function of Eq. (10). The finite-temperature state of nuclear matter could be understood as the state that there are a great number of coupling nucleons, antinucleons and mesons in the perturba- tion vacuum, so the noninteracting propagators in vacuum are used in the calculation of the self-energies of particles. The momentum-space noninteracting propagators of the scalar meson, vector meson and nucleon in perturbation vacuum j 0 i follow as: −1 i∆0(p) = 2 2 ; (11) p − mσ + i" µν µν g iD0 (p) = 2 2 ; (12) p − m! + i" αβ −1 iG0 (p) = µ : (13) γµp − MN + i" Since the vector meson couples to the conserved baryon current, the longitudinal part in the propagator of the vector meson will not contribute to physical quantities[3, 13]. Therefore, only the transverse part in the propagator of the vector meson is written in Eq. (12). According to Eq. (1), the interaction Hamiltonian can be expressed as µ HI = gσ ¯σ + g! ¯γµ! : (14) 5 In the second order approximation, only 2 (−i) 4 4 S^2 = d x1 d x2T [HI (x1)HI (x2)] (15) 2! Z Z in the S-matrix should be calculated in order to obtain the self-energy corrections of the nucleon and mesons. The coupling constants gσ, g!, the masses of mesons mσ, m! and the nucleon mass MN are supposed to have been renormalized, then the contributions of the nucleon-loop diagrams are not needed to be considered[13, 14]. Only the terms with one contraction of two fields in the Wick expansions of S^2 should be calculated. Thus with the similar procedure of Ref.[10, 11, 12], the scalar meson self-energy Σσ, the vector meson self-energy + − Σ!, the nucleon self-energy Σ and the antinucleon self-energy Σ in the hot and dense nuclear matter are obtained. The second order self-energy of the scalar meson is d3p M Σ = (−ig )2 N σ σ (2π)3 E(p) λX=1;2 Z nF U¯(p; λ) (iG0(p − k) + iG0(p + k)) U(p; λ) h − n¯F V¯ (p; λ) (iG0(−p − k) + iG0(−p + k)) V (p; λ) d3p M i = g2 N σ (2π)3 E(p) λX=1;2 Z 1 1 nF U¯(p; λ) + U(p; λ) " p/ − k/ − MN p/ + k/ − MN ! 1 1 − n¯F V¯ (p; λ) + V (p; λ) ; (16) −p/ − k/ − MN −p/ + k/ − MN ! # where U(p; λ) and V (p; λ) are the Dirac spinors of the nucleon and the antinucleon, respectively, and U¯(p; λ) and V¯ (p; λ) are their conjugate spinors, respectively. p/ + M U(p; λ)U¯(p; λ) = N ; (17) 2MN λX=1;2 −p/ + M −V (p; λ)V¯ (p; λ) = N : (18) 2MN λX=1;2 6 The second order self-energy of the vector meson is d3p M −g Σ = (−ig )2 N µν ! ! (2π)3 E(p) λX=1;2 Z nF U¯(p; λ) (γνiG0(p − k)γµ + γµiG0(p + k)γν) U(p; λ) h − n¯F V¯ (p; λ) (γνiG0(−p − k)γµ + γµiG0(−p + k)γν) V (p; λ) d3p M i = g 2 N ! (2π)3 E(p) λX=1;2 Z 1 1 nF U¯(p; λ) γν γµ + γµ γν U(p; λ) " p/ − k/ − MN p/ + k/ − MN ! 1 1 − n¯F V¯ (p; λ) γν γµ + γµ γν V (p; λ) :(19) −p/ − k/ − MN −p/ + k/ − MN ! # The second order self-energy of the nucleon is + + + + Σ = Σs;1 + Σs;2 + Σs;3 ; (20) s=σ;! X in which d3p M Σ+ = (−ig )2 N i∆ (0) σ;1 σ (2π)3 E(p) 0 λX=1;2 Z nF U¯(p; λ)U(p; λ) − n¯F V¯ (p; λ)V (p; λ) h 2 i gσ = − 2 ρS; (21) mσ where ρS is the scalar density of protons or neutrons, 2 3 MN ρS = d p (nF + n¯F ) ; (22) (2π)3 2 2 Z p~ + MN q d3p M Σ+ = g2 N σ;2 σ (2π)3 E(p) λX=1;2 Z nF U(p; λ) i∆0(k − p) U¯(p; λ) − n¯F V (p; λ) i∆0(k + p) V¯ (p; λ) (23) h 3 i 2 d p MN p/ + MN 1 p/ − MN 1 = −gσ 3 nF 2 2 − n¯F 2 2 ; Z (2π) E(p) " 2MN (k − p) − mσ 2MN (k + p) − mσ # 3 + 2 d k Σσ;3 = (−igσ) 3 nσ (iG0(p − k) + iG0(p + k)) Z 2Ωσ(2π) 3 2 d k 1 1 = gσ 3 nσ + ; (24) Z 2Ωσ(2π) p/ − k/ − MN p/ + k/ − MN ! 7 d3p M Σ+ = (−ig )2 N γ iDµν(0) !;1 ! (2π)3 E(p) µ 0 λX=1;2 Z nF U¯(p; λ)γνU(p; λ) − n¯F V¯ (p; λ)γνV (p; λ) h 2 i g! = γ0 2 ρB; (25) m! where ρV defined in Eq.
Load more

Recommended publications
  • Advances in Quantum Field Theory
    ADVANCES IN QUANTUM FIELD THEORY Edited by Sergey Ketov Advances in Quantum Field Theory Edited by Sergey Ketov Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Romana Vukelic Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published February, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from [email protected] Advances in Quantum Field Theory, Edited by Sergey Ketov p.
    [Show full text]
  • Super-Exceptional Embedding Construction of the Heterotic M5
    Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector Domenico Fiorenza, Hisham Sati, Urs Schreiber June 2, 2020 Abstract A new super-exceptional embedding construction of the heterotic M5-brane’s sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green- Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond that, further fields and interactions emerge in the model, arising from probe M2- and probe M5-brane wrapping modes. Here we classify the full super-exceptional field content and work out some of its characteristic interactions from the rich super-exceptional Lagrangian of the model. We show that SU(2) U(1)-valued scalar and vector fields emerge from probe M2- and M5-branes wrapping × the vanishing cycle in the A1-type singularity; together with a pair of spinor fields of U(1)-hypercharge 1 and each transforming as SU(2) iso-doublets. Then we highlight the appearance of a WZW-type term in± the super-exceptional PS-Lagrangian and find that on the electromagnetic field it gives the first-order non-linear DBI-correction, while on the iso-vector scalar field it has the form characteristic of the coupling of vector mesons to pions via the Skyrme baryon current. We discuss how this is suggestive of a form of SU(2)-flavor chiral hadrodynamics emerging on the single (N = 1) M5 brane, different from, but akin to, holographiclarge-N QCD.
    [Show full text]
  • A Quark-Meson Coupling Model for Nuclear and Neutron Matter
    Adelaide University ADPT February A quarkmeson coupling mo del for nuclear and neutron matter K Saito Physics Division Tohoku College of Pharmacy Sendai Japan and y A W Thomas Department of Physics and Mathematical Physics University of Adelaide South Australia Australia March Abstract nucl-th/9403015 18 Mar 1994 An explicit quark mo del based on a mean eld description of nonoverlapping nucleon bags b ound by the selfconsistent exchange of ! and mesons is used to investigate the prop erties of b oth nuclear and neutron matter We establish a clear understanding of the relationship b etween this mo del which incorp orates the internal structure of the nucleon and QHD Finally we use the mo del to study the density dep endence of the quark condensate inmedium Corresp ondence to Dr K Saito email ksaitonuclphystohokuacjp y email athomasphysicsadelaideeduau Recently there has b een considerable interest in relativistic calculations of innite nuclear matter as well as dense neutron matter A relativistic treatment is of course essential if one aims to deal with the prop erties of dense matter including the equation of state EOS The simplest relativistic mo del for hadronic matter is the Walecka mo del often called Quantum Hadro dynamics ie QHDI which consists of structureless nucleons interacting through the exchange of the meson and the time comp onent of the meson in the meaneld approximation MFA Later Serot and Walecka extended the mo del to incorp orate the isovector mesons and QHDI I and used it to discuss systems like
    [Show full text]
  • Relativistic Nuclear Field Theory and Applications to Single- and Double-Beta Decay
    Relativistic nuclear field theory and applications to single- and double-beta decay Caroline Robin, Elena Litvinova INT Neutrinoless double-beta decay program Seattle, June 13, 2017 Outline Relativistic Nuclear Field Theory: connecting the scales of nuclear physics from Quantum Hadrodynamics to emergent collective phenomena Nuclear response to one-body isospin-transfer external field: Gamow-Teller transitions, beta-decay half-lives and the “quenching” problem Current developments: ground-state correlations in RNFT Application to double-beta decay: some ideas Conclusion & perspectives Outline Relativistic Nuclear Field Theory: connecting the scales of nuclear physics from Quantum Hadrodynamics to emergent collective phenomena Nuclear response to one-body isospin-transfer external field: Gamow-Teller transitions, beta-decay half-lives and the “quenching” problem Current developments: ground-state correlations in RNFT Application to double-beta decay: some ideas Conclusion & perspectives Relativistic Nuclear Field Theory: foundations Quantum Hadrodynamics σ ω ρ - Relativistic nucleons mesons self-consistent m ~140-800 MeV π,σ,ω,ρ extensions of the Relativistic Relativistic mean-field Mean-Field nucleons + superfluidity via S ~ 10 MeV Green function n techniques (1p-1h) collective vibrations successive (phonons) ~ few MeV Relativistic Random Phase Approximation corrections in the single- phonon particle motion (2p-2h) and effective interaction Particle-Vibration coupling - Nuclear Field theory nucleons – Time-Blocking & phonons ... (3p-3h)
    [Show full text]
  • The Role of Nucleon Structure in Finite Nuclei
    ADP-95-45/T194 THE ROLE OF NUCLEON STRUCTURE IN FINITE NUCLEI Pierre A. M. GUICHON 1 DAPHIA/SPhN, CE Saclay, 91191 Gif-sur Yvette, CEDEX, France Koichi SAITO 2 Physics Division, Tohoku College of Pharmacy Sendai 981, Japan Evguenii RODIONOV 3 and Anthony W. THOMAS 4 Department of Physics and Mathematical Physics, University of Adelaide, South Australia 5005, Australia arXiv:nucl-th/9509034v2 15 Jan 1996 PACS numbers: 12.39.Ba, 21.60.-n, 21.90.+f, 24.85.+p Keywords: Relativistic mean-field theory, finite nuclei, quark degrees of freedom, MIT bag model, charge density [email protected] [email protected] [email protected] [email protected] 1 Abstract The quark-meson coupling model, based on a mean field description of non- overlapping nucleon bags bound by the self-consistent exchange of σ, ω and ρ mesons, is extended to investigate the properties of finite nuclei. Using the Born- Oppenheimer approximation to describe the interacting quark-meson system, we derive the effective equation of motion for the nucleon, as well as the self-consistent equations for the meson mean fields. The model is first applied to nuclear matter, after which we show some initial results for finite nuclei. 2 1 Introductory remarks The nuclear many-body problem has been the object of enormous theoretical attention for decades. Apart from the non-relativistic treatments based upon realistic two-body forces [1, 2], there are also studies of three-body effects and higher [3]. The importance of relativity has been recognised in a host of treatments under the general heading of Dirac- Brueckner [4, 5, 6].
    [Show full text]
  • Structure of the Vacuum in Nuclear Matter: a Nonperturbative Approach
    PHYSICAL REVIEW C VOLUME 56, NUMBER 3 SEPTEMBER 1997 Structure of the vacuum in nuclear matter: A nonperturbative approach A. Mishra,1,* P. K. Panda,1 S. Schramm,2 J. Reinhardt,1 and W. Greiner1 1Institut fu¨r Theoretische Physik, J.W. Goethe Universita¨t, Robert Mayer-Straße 10, Postfach 11 19 32, D-60054 Frankfurt/Main, Germany 2Gesellschaft fu¨r Schwerionenforschung (GSI), Planckstraße 1, Postfach 110 552, D-64220 Darmstadt, Germany ~Received 3 February 1997! We compute the vacuum polarization correction to the binding energy of nuclear matter in the Walecka model using a nonperturbative approach. We first study such a contribution as arising from a ground-state structure with baryon-antibaryon condensates. This yields the same results as obtained through the relativistic Hartree approximation of summing tadpole diagrams for the baryon propagator. Such a vacuum is then generalized to include quantum effects from meson fields through scalar-meson condensates which amounts to summing over a class of multiloop diagrams. The method is applied to study properties of nuclear matter and leads to a softer equation of state giving a lower value of the incompressibility than would be reached without quantum effects. The density-dependent effective s mass is also calculated including such vacuum polarization effects. @S0556-2813~97!02509-0# PACS number~s!: 21.65.1f, 21.30.2x I. INTRODUCTION to be developed to consider nuclear many-body problems. The present work is a step in that direction including vacuum Quantum hadrodynamics ~QHD! is a general framework polarization effects. for the nuclear many-body problem @1–3#.
    [Show full text]
  • Hadron–Quark Phase Transition in the SU (3) Local Nambu–Jona-Lasinio (NJL) Model with Vector Interaction
    S S symmetry Article Hadron–Quark Phase Transition in the SU (3) Local Nambu–Jona-Lasinio (NJL) Model with Vector Interaction Grigor Alaverdyan Department of Radio Physics, Yerevan State University, 1 Alex Manoogian Street, Yerevan 0025, Armenia; [email protected] Abstract: We study the hadron–quark hybrid equation of state (EOS) of compact-star matter. The Nambu–Jona-Lasinio (NJL) local SU (3) model with vector-type interaction is used to describe the quark matter phase, while the relativistic mean field (RMF) theory with the scalar-isovector d-meson effective field is adopted to describe the hadronic matter phase. It is shown that the larger the vector coupling constant GV, the lower the threshold density for the appearance of strange quarks. For a sufficiently small value of the vector coupling constant, the functions of the mass dependence on the baryonic chemical potential have regions of ambiguity that lead to a phase transition in nonstrange quark matter with an abrupt change in the baryon number density. We show that within the framework of the NJL model, the hypothesis on the absolute stability of strange quark matter is not realized. In order to describe the phase transition from hadronic matter to quark matter, Maxwell’s construction is applied. It is shown that the greater the vector coupling, the greater the stiffness of the EOS for quark matter and the phase transition pressure. Our results indicate that the infinitesimal core of the quark phase, formed in the center of the neutron star, is stable. Keywords: quark matter; NJL model; RMF theory; deconfinement phase transition; Maxwell con- struction Citation: Alaverdyan, G.
    [Show full text]
  • Exploring the Isovector Equation of State at High Densities with HIC
    INT program Interfaces between structure and reactions for rare isotopes and nuclear astrophysics Seattle, August 8 - September 2, 2011 Exploring the isovector equation of state at high densities with HIC Vaia D. Prassa Aristotle University of Thessaloniki Department of Physics Introduction Quantum Hadrodynamics (QHD) Transport theory Particle Production Summary & Outlook Outline 1 Introduction Nuclear Equation of state Symmetry Energy Phase diagram Spacetime evolution 2 Quantum Hadrodynamics (QHD) Meson exchange model Asymmetric Nuclear Equation of State 3 Transport theory Vlasov term Collision term 4 Particle Production Cross sections Kaon-nucleon potential 5 Summary & Outlook Vaia D. Prassa Exploring the isovector equation of state at high densities with HIC 2 Introduction Nuclear Equation of state Quantum Hadrodynamics (QHD) Symmetry Energy Transport theory Phase diagram Particle Production Spacetime evolution Summary & Outlook First questions to be answered: Why is the Symmetry Energy so important? At low densities: Nuclear structure (neutron skins, pigmy resonances), Nuclear Reactions (neutron distillation in fragmentation, charge equilibration), and Astrophysics, (neutron star formation, and crust), At high densities: Relativistic Heavy ion collisions (isospin flows, particle production), Compact stars (neutron star structure), and for fundamental properties of strong interacting systems (transition to new phases of the matter). Why HIC? Probing the in-medium nuclear interaction in regions away from saturation. Reaction observables sensitive to the symmetry term of the nuclear equation of state. High density symmetry term probed from isospin effects on heavy ion reactions at relativistic energies. In this talk: HIC at intermediate energies 400AMeV -2AGeV . Investigation of particle ratios: Probes for the symmetry energy density dependence. In-medium effects in inelastic cross sections & Kaon potential choices.
    [Show full text]
  • Classical and Quantum Mechanics Via Lie Algebras, Cambridge University Press, to Appear (2009?)
    Classical and quantum mechanics via Lie algebras Arnold Neumaier Dennis Westra University of Vienna, Austria April 14, 2011 arXiv:0810.1019v2 [quant-ph] 14 Apr 2011 This is the draft of a book. The manuscript has not yet full book quality. Please refer to the book once it is published. Until then, we’d appreciate suggestions for improvements; please send them to [email protected] copyright c by Arnold Neumaier and Dennis Westra Contents Preface ix I An invitation to quantum mechanics 1 1 Motivation 3 1.1 Classicalmechanics................................ 3 1.2 Relativitytheory ................................. 5 1.3 Statistical mechanics and thermodynamics . ... 7 1.4 Hamiltonianmechanics.............................. 8 1.5 Quantummechanics ............................... 10 1.6 Quantumfieldtheory............................... 13 1.7 TheSchr¨odingerpicture . .. .. 13 1.8 TheHeisenbergpicture.............................. 15 1.9 Outlineofthebook................................ 17 2 The simplest quantum system 25 2.1 Matrices, relativity and quantum theory . .. 26 2.2 Continuousmotionsandmatrixgroups . 28 2.3 Infinitesimal motions and matrix Lie algebras . 29 2.4 Uniform motions and the matrix exponential . .. 31 2.5 Volume preservation and special linear groups . ... 33 2.6 The vector product, quaternions, and SL(2, C)................. 35 i ii CONTENTS 2.7 The Hamiltonian form of a Lie algebra . 38 2.8 Atomic energy levels and unitary groups . 39 2.9 QubitsandBlochsphere ............................. 40 2.10 Polarized light and beam transformations . ... 41 2.11 Spinandspincoherentstates . 44 2.12 Particles and detection probabilities . .. 47 2.13Photonsondemand................................ 48 2.14 Unitary representations of SU(2) ........................ 53 3 The symmetries of the universe 57 3.1 Rotations and SO(n)............................... 57 3.2 3-dimensional rotations and SO(3) ......................
    [Show full text]
  • From Nuclear Matter to Neutron Stars
    The University of Adelaide Thesis submitted for the degree of Doctor of Philosophy in Theoretical Physics Department of physics and Special research centre for the subatomic structure of matter Hadrons and Quarks in Dense Matter: From Nuclear Matter to Neutron Stars Supervisors: Author: Prof. A. W. Thomas Daniel L. Whittenbury Prof. A. G. Williams Dr R. Young November 10, 2015 Contents List of Tables vii List of Figures ix Signed Statement xv Acknowledgements xvii Dedication xix Abstract xxi List of Publications xxiii 1 Introduction 1 2 From Nuclear Physics to QCD and Back Again 9 2.1 NN Interaction and Early Nuclear Physics . .9 2.2 Basic Notions of Quantum Chromodynamics . 16 2.2.1 QCD Lagrangian and its Symmetries . 17 2.2.2 Asymptotic Freedom and Perturbation Theory . 21 2.2.3 Chiral Effective Field Theory . 24 2.3 Nuclear Matter . 25 2.4 Experimental and Theoretical Knowledge of the Nuclear EoS . 30 2.5 Quantum Hadrodynamics and the Relativistic Mean Field Approximation 35 2.6 The Quark-Meson Coupling Model . 42 3 General Relativity and the Astrophysics of Neutron Stars 47 3.1 Hydrostatic Equilibrium . 49 3.2 The Neutron Star EoS . 51 4 Hartree-Fock QMC Applied to Nuclear Matter 57 4.1 The Hartree-Fock QMC . 58 4.2 The Lagrangian Density . 59 4.3 Equations of Motion and the MFA . 61 4.4 The Hamiltonian Density . 62 4.5 Hartree-Fock Approximation . 64 4.6 The In-medium Dirac Equation . 72 iii 4.7 Detailed Evaluation of σ Meson Fock Term . 73 4.8 Final Expressions for the Fock Terms .
    [Show full text]
  • Curriculum Vitae December 27, 2018
    Curriculum Vitae December 27, 2018 Name: Xilin Zhang Email: [email protected] Address: Physics Research Building, 191 West Woodruff Avenue, Columbus, Ohio 43210 Education: Degree Institution Date Ph. D. Indiana University, Bloomington, IN, USA 2007{08, Thesis: Electroweak interactions and the Delta resonance 2010{12 in a Chiral effective field theory for nuclei Advisors: Brian D. Serot and Jinfeng Liao M. S. Indiana University, Bloomington, IN, USA 2005{07 Academic Positions: Position Institution Date Postdoc Research Associate Physics Department 2018{ The Ohio State Univ., Columbus, OH, USA Postdoc Research Associate Physics Department 2015{2018 University of Washington, Seattle, WA, USA Intensity Frontier Fellow Fermi National Accelerator Laboratory 2014 Batavia, IL, USA Postdoc Research Associate Physics Department 2012{14 Ohio University, Athens, OH, USA Position Institution Date Research Assistant Nuclear Theory Center 2007{08, Indiana University, Bloomington, IN, USA 2010{11 Teaching Assistant and Physics Department 2005{08 Associate Instructor Indiana University, Bloomington, IN, USA 1 Awards and Honors: 1. Intensity Frontier Fellowship, Fermi National Accelerator Laboratory, Batavia, IL, 2014. 2. Outstanding Graduate Student in Theoretical Research, Physics Department, Indiana University, 2011. 3. Outstanding Student Award, Department of Modern Physics, University of Science and Technolgy of China, 2001, 2002, 2003, and 2004. Research Interests: • Light nuclei: (1) effective field theory (EFT) approach for studying low-energy reac- tions with astrophysical relevance; (2) factorization of long- and short-distance physics and its usage in studying higher-energy reactions; (3) ab initio reaction calculation by merging EFT with ab initio structure calculation; (4) Bayesian-inference-based uncer- tainty estimation for treating experimental and computational data.
    [Show full text]
  • Relativistic Mean Fields in the Early Universe
    Relativistic Mean Fields in the Early Universe A thesis submitted in partial fulfillment of the requirement for the degree of Bachelor of Science with Honors in Physics from the College of William and Mary in Virginia, by Sarp Akcay Accepted for (Honors, High Honors or Highest Honors) Advisor: Professor John Dirk Walecka Dr. Keith Griffioen Dr. Nahum Zobin Williamsburg, Virginia May 2002 Abstract Our goal is to investigate what changes occur in the standard big bang model for the early universe if we include relativistic mean fields to describe the nuclear interactions. We work in the “nuclear regime” located between 10¡4 and 10¡1 seconds after time-zero, where the energy scale is between 200 MeV and 10 MeV. This is the interval, in which the universe was very hot, dense, and filled with baryons, mesons, and leptons coupled with a uniform gas of photons. It is in this regime that we will use quantum hadrodynamics (QHD) to study the effects of relativistic mean fields in several weak and nuclear reactions that have been firmly established by the standard big bang model (SBBM). QHD is an effective field theory for the underlying theory of quantum chromodynamics (QCD). We construct a local lagrangian in infinite nuclear matter with constant scalar and vector fields with no spatial dependence. These new fields of QHD bring about changes in thermal properties of the early universe as well as in interaction cross sections as we shall demonstrate. It is not clear what effects, if any, these changes have on the subsequently cooled cosmos. i Acknowledgements I would first like to thank to Professor Dirk Walecka for his patience and guidance during the making of this project.
    [Show full text]