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作者 Meyer-Ortmanns, Hildegard
書名 Principles of Phase Structures in Particle Physics : The Phase Structure of QCD
出版項 Singapore : World Scientific Publishing Co Pte Ltd, 2006
©2006
國際標準書號 9789812774910 (electronic bk.)
9789810234416
book jacket
說明 1 online resource (702 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 World Scientific Lecture Notes in Physics Ser. ; v.77
World Scientific Lecture Notes in Physics Ser
附註 Intro -- Contents -- Preface -- 1. Introduction -- 2. General Background from Statistical Physics -- 2.1 Generalities -- 2.1.1 Phase transitions in statistical systems -- 2.1.1.1 First- and second-order transitions in the infinite volume limit -- 2.1.1.2 Landau's free energy -- 2.2 Generating functional n-point correlations and effective potentials -- 2.3 The molecular-mean field approximation -- 2.3.1 Self-consistent equation of state for a ferromagnet -- 2.3.1.1 Critical exponents in the molecular-mean field approximation -- 2.3.2 Variational estimates for the free energy of a spin system -- 2.3.3 Molecular-mean field approximation for an N-component scalar field theory in D dimensions -- 2.3.3.1 Solutions of the mean-field equations -- 2.3.3.2 Critical exponents in the symmetric phase -- 2.3.3.3 Critical exponents in the broken phase -- 2.3.3.4 First-order transitions within the molecular-mean field approximation -- 2.3.3.5 Tricritical behavior -- 2.3.4 Variational estimates for the SU(2) Higgs model -- 2.3.4.1 Solutions of the mean-field equations of the SU(2) Higgs model -- 2.3.5 Improved variational estimates for the SU(2) Higgs model -- 2.3.6 Summary -- 2.4 Renormalization group -- 2.4.1 Generalities -- 2.4.2 Block-spin transformations -- 2.4.3 Iteration of the block-spin transformation -- 2.4.4 Field renormalization -- 2.4.5 Linearized renormalization-group transformation and universality -- 2.4.6 Scaling-sum rules -- 2.4.6.1 Anomalous dimension -- 2.4.6.2 Correlation length -- 2.4.6.3 Two-point susceptibility -- 2.4.6.4 Vacuum expectation value -- 2.4.6.5 Specific heat -- 2.4.6.6 Summary -- 2.4.7 Violation of scaling-sum rules for critical exponents -- 2.5 Finite-size scaling analysis for second-order phase transitions -- 2.5.1 Shift in the pseudo-critical parameter -- 2.5.2 T-like and h-like scaling fields
2.6 Finite-size scaling analysis for first-order phase transitions -- 2.6.1 Predictions for rounding and shifting of singularities in first-order transitions -- 2.6.2 Finite-size scaling with linked cluster expansions -- 2.6.3 Summary of criteria -- 3. Field Theoretical Framework for Models in Particle Physics -- 3.1 The standard model in limiting cases I: Spin models as a guideline for the phase structure of QCD -- 3.1.1 Renormalization-group analysis in the chiral limit -- 3.1.1.1 Renormalization-group equation scaling behavior of the Green functions and zeros of the B-function -- 3.1.1.2 Computation of the B-function for an O(N)-symmetric scalar field theory -- 3.1.1.3 Generalization to the SU(N1) x SU(N1)- symmetric model -- 3.1.1.4 Including nonzero bare masses -- 3.1.2 Limit of the pure SU(Nc) gauge theory -- 3.1.2.1 Effective versus physical temperatures -- 3.1.2.2 The phase structure of Z(N)-spin models -- 3.1.2.3 Influence of dynamical quarks -- 3.1.2.4 Finite quark masses and external fields -- 3.1.2.5 Summary -- 3.1.2.6 The Columbia plot -- 3.2 The standard model in limiting cases II: Phase transitions in the electroweak part of the standard model -- 3.2.1 The electroweak phase transition in cosmology -- 3.2.2 Perturbative approach in four dimensions in the continuum -- 3.2.3 The lattice approach in four dimensions -- 3.2.3.1 Gross phase structure with deconfinement and Higgs transition -- 3.2.3.2 The Higgs transition in four dimensions -- 3.2.3.3 Effect of the gauge fields -- 3.2.4 The lattice approach in three dimensions -- 3.2.4.1 Measurements of the surface tension -- 3.2.4.2 Localization of the critical endpoint -- 3.2.4.3 Universality class of the critical endpoint -- 3.2.5 Summary of results and open questions -- 3.3 A primer to lattice gauge theory -- 3.3.1 The QCD Lagarngian -- 3.3.2 Introducing the lattice cutoff
3.3.3 Scalar field theories on the lattice -- 3.3.4 Gauge field theories on the lattice -- 3.3.4.1 Functional measure and the gauge orbit -- 3.3.5 Fermions on the lattice -- 3.3.5.1 The Wilson-fermion action and hopping parameters -- 3.3.5.2 Staggered fermions and flavor symmetries -- 3.3.5.3 Sources of errors -- 3.3.6 Translating lattice results to continuum physics -- 3.3.6.1 The critical temperature Tc -- 3.3.6.2 Choosing the appropriate extension in time direction -- 3.3.6.3 A test of asymptotic scaling -- 3.3.6.4 Translation to physical units -- 3.3.7 Summary and outlook -- 3.3.8 Transfer matrix and Polyakov loops -- 3.3.8.1 Path integral formulation of finite temperature field theory -- 3.3.8.2 Quantum mechanics of gluons -- 3.3.8.3 Finite-temperature partition function -- 3.3.8.4 Representation as path integral -- 4. Analytic Methods on the Lattice and in the Continuum -- 4.1 Convergent versus asymptotic expansions -- 4.1.1 Asymptotic expansions -- 4.1.2 Borel resummations -- 4.1.3 Polymer expansions -- 4.1.4 Strong coupling expansions -- 4.1.5 A theorem by Osterwalder and Seiler -- 4.1.6 Linked cluster expansions as convergent expansions -- 4.1.7 Convergent power series and the critical region: radius of convergence and physical singularity -- 4.2 Linked cluster expansions in more detail -- 4.2.1 Historical remarks -- 4.2.2 Introduction to linked cluster expansions -- 4.2.3 Classification of graphs -- 4.2.4 Towards a computer implementation of graphs -- 4.2.5 Application to phase transitions and critical phenomena -- 4.2.6 Some results -- 4.3 Renormalization perturbation theory and universality at zero temperature - the continuum limit -- 4.3.1 Generalities -- 4.3.2 Renormalization -- 4.3.3 Perturbative renormalization -- 4.3.4 The counterterm approach -- 4.3.5 Power counting in the continuum
4.3.6 Power counting for Feynman integrals in momentum space: UV-divergence for rational functions and integrals -- 4.3.7 Power counting for Feynman diagrams: UV-divergence degrees of propagators vertices fields and diagrams -- 4.3.8 Renormalization or: Removing UV-divergencies under the integral sign -- 4.3.9 Renormalization or: Removing UV-divergencies in the counterterm approach -- 4.3.10 Power counting in lattice field theory -- 4.3.11 Preliminaries of lattice-power counting and lattice UV-divergence degrees -- 4.3.12 Power-counting theorem on the lattice -- 4.3.13 Renormalization on the lattice -- 4.3.14 Massless fields and IR-power counting -- 4.3.15 Gauge theories -- 4.4 Weak coupling expansion at finite temperature -- 4.4.1 Motivation and problems -- 4.4.2 Finite-temperature Feynman rules and renormalization -- 4.4.3 IR-divergencies and resummation techniques -- 4.4.4 Resummation leading to a reasonable weak coupling expansion -- 4.4.5 Gauge theories and the magnetic-mass problem -- 4.4.6 Hard-thermal loop resummation -- 4.4.6.1 Example of a hard-thermal loop -- 4.4.6.2 Effective HTL-action -- 4.5 Constraint effective potential and gap equations -- 4.5.1 Generalities -- 4.5.2 Scalar field theories -- 4.5.2.1 Mass resummation and gap equations -- 4.5.3 The order of the phase transition -- 4.5.4 The weak-electroweak phase transition -- 4.6 Dimensional reduction at high temperature -- 4.6.1 Generalities -- 4.6.2 Matsubara decomposition and the Appelquist-Carazzone decoupling theorem -- 4.6.3 General outline of dimensional reduction -- 4.6.4 Dimensional reduction of a O4-theory from four to three dimensions -- 4.6.4.1 Large-cutoff and high-temperature expansions of one-loop integrals -- 4.6.4.2 The steps after dimensional reduction -- 4.6.5 Pure gauge theories and QCD -- 4.6.5.1 Pure gauge theories -- 4.6.5.2 QCD with fermions
4.6.5.3 Dimensional reduction for pure SU(Nc) gauge theories -- 4.6.5.4 Renormalization and zero-momentum projection -- 4.6.5.5 Nonperturbative verification of dimensional reduction and determination of the screening masses -- 4.6.5.6 Dimensional reduction in QCD with dynamical fermions -- 4.6.6 The Gross-Neveu model in three dimensions -- 4.6.6.1 Large N -- 4.6.6.2 Phase structure at infinite N -- 4.6.6.3 Dimensional reduction for finite N -- 4.6.6.4 Phase structure at finite N -- 4.6.6.5 The strong-coupling limit -- 4.6.6.6 Finite couplings and LCE-expansions -- 4.6.6.7 Summary -- 4.6.7 Dimensional reduction in the SU(2) Higgs model -- 4.6.7.1 Guidelines for an alternative form of dimensional reduction -- 4.6.7.2 Performing the integration step -- 4.6.7.3 Integrating upon the superheavy modes -- 4.6.7.4 Examples for the matching procedure to integrate upon the superheavy modes -- 4.6.7.5 Integrating upon the heavy modes -- 4.7 Flow equations of Polchinski -- 4.7.1 Generalities -- 4.7.2 Flow equations for effective interactions -- 4.7.3 Effective average action -- 4.7.4 High-temperature phase transition of O(N) models -- 4.7.5 Appendix: Perturbative renormalization -- 5. Numerical Methods in Lattice Field Theories -- 5.1 Algorithms for numerical simulations in lattice field theories -- 5.2 Pitfalls on the lattice -- 5.3 Pure gauge theory: The order of the SU(3)-deconfinement transition -- 5.3.1 The order of limits -- 5.3.2 Correlation lengths mass gaps and tunneling events -- 5.3.3 Correlation functions in the pure SU(3) gauge theory -- 5.4 Including dynamical fermions -- 5.4.1 Finite-size scaling analysis -- 5.4.2 Finite-mass scaling analysis -- 5.4.3 Bulk transitions -- 5.4.4 Results for two and three flavors: The physical mass point -- 5.5 Thermodynamics on the lattice -- 5.5.1 Thermodynamics for the pure gauge theory
5.5.2 Including dynamical fermions in thermodynamic observables
The phase structure of particle physics shows up in matter at extremely high densities and/or temperatures as they were reached in the early universe, shortly after the big bang, or in heavy-ion collisions, as they are performed nowadays in laboratory experiments. In contrast to phase transitions of condensed matter physics, the underlying fundamental theories are better known than their macroscopic manifestations in phase transitions. These theories are quantum chromodynamics for the strong interaction part and the electroweak part of the Standard Model for the electroweak interaction. It is their non-Abelian gauge structure that makes it a big challenge to predict the type of phase conversion between phases of different symmetries and different particle contents. The book is about a variety of analytical and numerical tools that are needed to study the phase structure of particle physics. To these belong convergent and asymptotic expansions in strong and weak couplings, dimensional reduction, renormalization group studies, gap equations, Monte Carlo simulations with and without fermions, finite-size and finite-mass scaling analyses, and the approach of effective actions as supplement to first-principle calculations. Sample Chapter(s). Chapter 1: Introduction (247 KB). Contents: General Background from Statistical Physics; Field Theoretical Framework for Models in Particle Physics; Analytic Methods on the Lattice and in the Continuum; Numerical Methods in Lattice Field Theories; Effective Actions in the Continuum; Phenomenological Applications to Relativistic Heavy-Ion Collisions. Readership: Theoretical and high energy physicists
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Meyer-Ortmanns, Hildegard Principles of Phase Structures in Particle Physics : The Phase Structure of QCD Singapore : World Scientific Publishing Co Pte Ltd,c2006 9789810234416
主題 Particles (Nuclear physics);Collisions (Nuclear physics)
Electronic books
Alt Author Reisz, Thomas
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