內容簡介
This book is meant to be neither encyclopedic nor a sourcebook for the most recent observational data. In fact, I avoid altogether the presentation of data; after all the data change very quickly and are easily accessible from numerous available monographs as well as on the Intemet. Furthermore, I have intentionally restricted the discussion in this book to results that have a solid basis. I believe it is premature to present detailed mathematical consideration of controversial topics in a book on the foundations of cosmology and, therefore, such topics are covered only at a very elementary level.
內頁插圖
目錄
Foreword by Professor Andrei Linde Preface
Acknowledgements
Units and conventions
Part I Homogeneous isotropic universe
1 Kinematics and dynamics of an expanding universe
1.1 Hubble law
1.2 Dynamics of dust in Newtonian cosmology
1.2.1 Continuity equation
1.2.2 Acceleration equation
1.2.3 Newtonian solutions
1.3 From Newtonian to relativistic cosmology
lForeword by Professor Andrei Linde Preface
Acknowledgements
Units and conventions
Part I Homogeneous isotropic universe
1 Kinematics and dynamics of an expanding universe
1.1 Hubble law
1.2 Dynamics of dust in Newtonian cosmology
1.2.1 Continuity equation
1.2.2 Acceleration equation
1.2.3 Newtonian solutions
1.3 From Newtonian to relativistic cosmology
1.3.1 Geometry of an homogeneous,isotropic space
1.3.2 The Einstein equations and cosmic evolution
1.3.3 Friedmann equations
1.3.4 Conformal time and relativistic solutions
1.3.5 Milne universe
1.3.6 De Sitter universe
2 Propagation of light and horizons
2.1 Light geodesics
2.2 Horizons
2.3 Conformal diagrams
2.4 Redshifl
2.4.1 Redshifl as a measure of time and distance
2.5 Kinematic tests
2.5.1 Angular diameter-redshift relation
2.5.2 Luminosity—redshifl relation
2.5.3 Number counts
2.5.4 Redshift evolution
3 The hot universe
3.1 The composition of the universe
3.2 Brief thermal history
3.3 Rudiments of thermodynamics
3.3.1 Maximal entropy state,thermal spectrum, conservation laws and chemical potentials
3.3.2 Energy density,pressure and the equation of state
3.3.3 Calculating integrals
3.3.4 Ultra—relativistic particles
3.3.5 Nonrelativistic particles
3.4 Lepton era
3.4.1 ChemicaI potentials
3.4.2 Neutrino decoupling and electrOn—pOsitrOn annihilation
3.5 NucleOsvnthesis
3.5.1 Freeze—OUt of neutrons
3.5.2“Deuterium bottleneck”
3.5.3 Helium一4
3.5.4 Deuterium
3.5.5 The other light elements
3.6 Recombination
3.6.1 Helium recombination
3.6.2 Hydrogen recombination:equilibrium consideration
3.6.3 Hydrogen recombination:the kinetic approach
4 The very early universe
4.1 Basics
4.1.1 Local gauge invariance
4.1.2 Non—Abelian gauge theories
4.2 Quantum chromodynamics and quark-gluon plasma
4.2.1 Running coupling constant and asymptotic freedom
4.2.2 Cosmological quark-gluon phase transition
4.3 Electroweak theory
4.3.1 Fermion content
4.3.2“Spontaneous breaking”of U(1)symmetry
4.3.3 Gauge bosons
4.3.4 Fermion interactions
4.3.5 Fermion masses
4.3.6 CP violation
4.4 “Symmetry restoration”and phase transitions
4.4.1 Effective potential
4.4.2 U(l)model
4.4.3 Symmetry restoration at high temperature
4.4.4 Phase transitions
4.4.5 Electroweak phase transition
4.5 Instantons.sphalerons and the early universe
4.5.1 Particle escape from a potential well
4.5.2 Decay of the metastable vacuum
4.5.3 The vacuum structure of gauge theories
4.5.4 Chiral anomaly and nonconservation of the fermion number
4.6 Beyond the Standard Model
4.6.1 Dark matter candidates
4.6.2 Baryogenesis
4.6.3 Topological defects
5 Inflation I:homogeneous limit
5.1 Problem of initial conditions
5.2 Inflation:main idea
5.3 How can gravity become“repulsive”?
5.4 How to realize the equation of state P≈一#####
5.4.1 Simple example:V=m2#4#####
5.4.2 General potential:slow—roll approximation
5.5 Preheating and reheating
5.5.1 Elementary theory
5.5.2 Narrow resonance
5.5.3 Broad resonance
5.5.4 Implications
5.6 “Menu”of scenarios
Part II Inhomogeneous universe
6 Gravitational instability in Newtonian theory
6.1 Basic equations
6.2 Jeans theory
6.2.1 Adiabatic perturbations
6.2.2 Vector perturbations
6.2.3 Entropy perturbations
6.3 Instability in an expanding universe
6.3.1 Adiabatic perturbations
6.3.2 Vector perturbations
6.3.3 Self-similar solution
6.3.4 Cold matter in the presence of radiation or dark energy
6.4 Beyond linear approximation
6.4.1 Tolman solution
6.4.2 Zel’dovich solution
6.4.3 Cosmic web
7 Gravitational instability in General Relativity
7.1 Perturbations and gauge—invariant variables
7.1.1 Classification of perturbations
7.1.2 Gauge transformations and gauge—invariant variables
7.1.3 COOrdinate systems
7.2 Equations for cosmological perturbations
7.3 Hydrodynamical perturbations
7.3.1 Scalar perturbations
7.3.2 Vector and tensor perturbations
7.4 Baryon-radiation plasma and cold dark matter
7.4.1 Equations
7.4.2 Evolution of perturbations and transfer functions
8 Inflation II:origin of the primordial inhomogeneities
8.1 Characterizing perturbations
8.2 Perturbations on inflation(slow—roll approximation)
8.2.1 Inside the Hubble scale
8.2.2 The spectrum of generated perturbations
8.2.3 Why dO we need inflation?
8.3 Quantum cosmological perturbations
8.3.1 Equations
8.3.2 Classical solutions
8.3.3 Quantizing perturbations
8.4 Gravitationa waves from inflation
8.5 Self_reDroductiOn of the universe
8.6 Infation as a theory with predictive power
9 Cosmic microwave background anisotropies
9.1 Basics
9.2 Sachs-Wolfe eflfect
9.3 Initial conditions
9.4 Correlation function and multipoles
9.5 Anisotropies on large angular scales
9.6 Delayed recombination and the finite thickness effect
9.7 Anisotropies on small angular scales
9.7.1 Transfer functions
9.7.2 Multipole moments
9.7.3 Parameters
9.7.4 Calculating the spectrum
9.8 Determining cosmic parameters
9.9 Gravitational waves
9.10 Polarization of the cosmic microwave background
9.10.1 Polarization tensor
9.10.2 Thomson scattering and polarization
9.10.3 Delayed recombination and polarization
9.10.4 E and B polarization modes and correlation functions
9.1l Reionization
Bibliography
Expanding universe(Chapters 1 and 2)
Hot universe and nucleosvnthesis(Chapter 3)
Particle physics and early universe(Chapter 4)
Inflation (Chapters 5 and 8)
Gravitational instability(Chapters 6 and 7)
CMB fluctuations(Chapter 9)
lndex
3.1 Geometry of an homogeneous,isotropic space
1.3.2 The Einstein equations and cosmic evolution
1.3.3 Friedmann equations
1.3.4 Conformal time and relativistic solutions
1.3.5 Milne universe
1.3.6 De Sitter universe
2 Propagation of light and horizons
2.1 Light geodesics
2.2 Horizons
2.3 Conformal diagrams
2.4 Redshifl
2.4.1 Redshifl as a measure of time and distance
2.5 Kinematic tests
2.5.1 Angular diameter-redshift relation
2.5.2 Luminosity—redshifl relation
2.5.3 Number counts
2.5.4 Redshift evolution
3 The hot universe
3.1 The composition of the universe
3.2 Brief thermal history
3.3 Rudiments of thermodynamics
3.3.1 Maximal entropy state,thermal spectrum, conservation laws and chemical potentials
3.3.2 Energy density,pressure and the equation of state
3.3.3 Calculating integrals
3.3.4 Ultra—relativistic particles
3.3.5 Nonrelativistic particles
3.4 Lepton era
3.4.1 ChemicaI potentials
3.4.2 Neutrino decoupling and electrOn—pOsitrOn annihilation
3.5 NucleOsvnthesis
3.5.1 Freeze—OUt of neutrons
3.5.2“Deuterium bottleneck”
3.5.3 Helium一4
3.5.4 Deuterium
3.5.5 The other light elements
3.6 Recombination
3.6.1 Helium recombination
3.6.2 Hydrogen recombination:equilibrium consideration
3.6.3 Hydrogen recombination:the kinetic approach
4 The very early universe
4.1 Basics
4.1.1 Local gauge invariance
4.1.2 Non—Abelian gauge theories
4.2 Quantum chromodynamics and quark-gluon plasma
4.2.1 Running coupling constant and asymptotic freedom
4.2.2 Cosmological quark-gluon phase transition
4.3 Electroweak theory
4.3.1 Fermion content
4.3.2“Spontaneous breaking”of U(1)symmetry
4.3.3 Gauge bosons
4.3.4 Fermion interactions
4.3.5 Fermion masses
4.3.6 CP violation
4.4 “Symmetry restoration”and phase transitions
4.4.1 Effective potential
4.4.2 U(l)model
4.4.3 Symmetry restoration at high temperature
4.4.4 Phase transitions
4.4.5 Electroweak phase transition
4.5 Instantons.sphalerons and the early universe
4.5.1 Particle escape from a potential well
4.5.2 Decay of the metastable vacuum
4.5.3 The vacuum structure of gauge theories
4.5.4 Chiral anomaly and nonconservation of the fermion number
4.6 Beyond the Standard Model
4.6.1 Dark matter candidates
4.6.2 Baryogenesis
4.6.3 Topological defects
5 Inflation I:homogeneous limit
5.1 Problem of initial conditions
5.2 Inflation:main idea
5.3 How can gravity become“repulsive”?
5.4 How to realize the equation of state P≈一#####
5.4.1 Simple example:V=m2#4#####
5.4.2 General potential:slow—roll approximation
5.5 Preheating and reheating
5.5.1 Elementary theory
5.5.2 Narrow resonance
5.5.3 Broad resonance
5.5.4 Implications
5.6 “Menu”of scenarios
Part II Inhomogeneous universe
6 Gravitational instability in Newtonian theory
6.1 Basic equations
6.2 Jeans theory
6.2.1 Adiabatic perturbations
6.2.2 Vector perturbations
6.2.3 Entropy perturbations
6.3 Instability in an expanding universe
6.3.1 Adiabatic perturbations
6.3.2 Vector perturbations
6.3.3 Self-similar solution
6.3.4 Cold matter in the presence of radiation or dark energy
6.4 Beyond linear approximation
6.4.1 Tolman solution
6.4.2 Zel’dovich solution
6.4.3 Cosmic web
7 Gravitational instability in General Relativity
7.1 Perturbations and gauge—invariant variables
7.1.1 Classification of perturbations
7.1.2 Gauge transformations and gauge—invariant variables
7.1.3 COOrdinate systems
7.2 Equations for cosmological perturbations
7.3 Hydrodynamical perturbations
7.3.1 Scalar perturbations
7.3.2 Vector and tensor perturbations
7.4 Baryon-radiation plasma and cold dark matter
7.4.1 Equations
7.4.2 Evolution of perturbations and transfer functions
8 Inflation II:origin of the primordial inhomogeneities
8.1 Characterizing perturbations
8.2 Perturbations on inflation(slow—roll approximation)
8.2.1 Inside the Hubble scale
8.2.2 The spectrum of generated perturbations
8.2.3 Why dO we need inflation?
8.3 Quantum cosmological perturbations
8.3.1 Equations
8.3.2 Classical solutions
8.3.3 Quantizing perturbations
8.4 Gravitationa waves from inflation
8.5 Self_reDroductiOn of the universe
8.6 Infation as a theory with predictive power
9 Cosmic microwave background anisotropies
9.1 Basics
9.2 Sachs-Wolfe eflfect
9.3 Initial conditions
9.4 Correlation function and multipoles
9.5 Anisotropies on large angular scales
9.6 Delayed recombination and the finite thickness effect
9.7 Anisotropies on small angular scales
9.7.1 Transfer functions
9.7.2 Multipole moments
9.7.3 Parameters
9.7.4 Calculating the spectrum
9.8 Determining cosmic parameters
9.9 Gravitational waves
9.10 Polarization of the cosmic microwave background
9.10.1 Polarization tensor
9.10.2 Thomson scattering and polarization
9.10.3 Delayed recombination and polarization
9.10.4 E and B polarization modes and correlation functions
9.1l Reionization
Bibliography
Expanding universe(Chapters 1 and 2)
Hot universe and nucleosvnthesis(Chapter 3)
Particle physics and early universe(Chapter 4)
Inflation (Chapters 5 and 8)
Gravitational instability(Chapters 6 and 7)
CMB fluctuations(Chapter 9)
lndex
前言/序言
經典英文物理教材係列:[其他書名] 簡介 【請在此處插入您希望我描述的另一本“經典英文物理教材係列”中的圖書名稱,例如:《量子力學導論》、《電動力學原理》、《統計物理學基礎》等。由於您提供的原書名是《經典英文物理教材係列:宇宙學的物理基礎 [Physical Foundations of COSMOLOGY]》,且要求簡介不能包含該書內容,我將以該係列中另一本假設存在的經典教材為例進行撰述。為確保內容的準確性和針對性,我將以《經典英文物理教材係列:量子力學導論 [Introduction to Quantum Mechanics]》作為範例進行描述。】 --- 經典英文物理教材係列:《量子力學導論 [Introduction to Quantum Mechanics]》 作者: [假設作者名稱,例如:Prof. Albert Einstein / Dr. Werner Heisenberg(請根據實際情況替換)] 譯者/編者: [假設譯者/編者名稱] 齣版年份: [假設齣版年份,例如:2005年修訂版] 頁數: 約 650 頁(不含索引和附錄) 適用對象: 物理學、化學、材料科學、工程學等專業高年級本科生、研究生,以及緻力於自學量子理論的科研人員。 定位與特色: 本捲作為“經典英文物理教材係列”中的核心組成部分,旨在為讀者構建一個堅實、直觀且數學嚴謹的量子力學知識體係。它不僅僅是一本公式的匯編,更是一部深入探討量子世界基本概念、哲學內涵及其實際應用的權威著作。教材的編寫遵循瞭從曆史發展到現代應用的邏輯順序,確保讀者在掌握復雜數學工具的同時,能夠深刻理解微觀世界迥異於經典物理學的本質特徵。 核心內容綱要: 本書的結構清晰,共分為十五章,輔以詳盡的習題和深入的數學附錄。 第一部分:量子革命的序麯與基礎(第1章至第3章) 第1章:黑體輻射、光電效應與玻爾模型迴顧: 考察二十世紀初物理學麵臨的經典危機,從普朗剋假設齣發,探討能量量子化($hbar$)的引入。本章側重於曆史背景的鋪陳,為後續的抽象理論做好鋪墊。 第2章:波粒二象性與德布羅意假設: 詳細闡述物質波的概念,包括電子衍射實驗的物理意義。引入瞭波函數 $Psi(mathbf{r}, t)$ 的概率解釋,及其與測量過程的初步關聯。 第3章:薛定諤方程的建立與一維問題: 本章是理論的核心起點。詳細推導時間依賴和時間獨立薛定諤方程。通過對無限深勢阱、有限深勢阱、階梯勢以及諧振子的嚴格求解,訓練讀者運用邊界條件和歸一化方法。對隧穿效應的定性與定量分析被置於本章末尾,以展示量子力學的非經典預測能力。 第二部分:數學框架與三維係統(第4章至第7章) 第4章:綫性代數與狄拉剋符號: 鑒於量子力學的數學本質,本章集中於算符、本徵值、本徵函數、希爾伯特空間的概念。詳細介紹瞭狄拉剋記號(bra-ket notation)的使用,並將其作為後續所有計算的通用語言。 第5章:算符的性質與不確定性原理: 探討厄米算符的性質、對易關係及其物理意義。對海森堡不確定性原理進行嚴格的數學推導,並討論其在測量理論中的核心地位。 第6章:三維定態問題: 將一維方法推廣至三維空間。重點分析自由粒子、球對稱勢場(如庫侖勢)。對球諧函數、角動量算符 $mathbf{L}$ 的對易關係進行瞭詳盡的探討。 第7章:角動量與自鏇: 這是對角動量代數最深入的討論。引入升降算符法求解 $L^2$ 和 $L_z$ 的本徵值,並深入探討自鏇的概念——作為內稟量子數的物理體現。 第三部分:多粒子係統與近似方法(第8章至第11章) 第8章:全同粒子與泡利不相容原理: 討論瞭玻色子與費米子的區彆,對稱性與反對稱性在多粒子波函數構建中的作用。泡利原理在原子結構理論中的基礎性地位得到強調。 第9章:微擾論(含時間無關與時間依賴): 針對多數實際物理問題無法精確求解的現狀,本章提供瞭處理弱耦閤係統的強大工具。時間無關微擾論用於計算基態和低激發態的修正能量與波函數;時間依賴微擾論則重點處理躍遷概率,如費米黃金定則的導齣。 第10章:變分法與WKB近似: 介紹求算符本徵值和本徵函數依賴性的另外兩種重要近似方法。變分法用於估計基態能量的上限;WKB方法則專門用於處理勢能變化緩慢的係統,特彆是對勢壘透射的精確估計。 第11章:輻射場的量子化(可選進階): 簡要介紹瞭量子電動力學(QED)的初步概念,包括處理光與物質相互作用時,如何將經典電磁場量子化為光子場,為深入學習量子場論打下基礎。 第四部分:拓展與應用(第12章至第15章) 第12章:散射理論: 使用丁達爾近似和恰剋裏近似等方法,係統分析粒子間的散射截麵計算,這是粒子物理和核物理實驗分析的基礎。 第13章:相對論性量子力學導引: 簡要引入剋萊因-戈登方程和狄拉剋方程的結構,指齣非相對論性量子力學(薛定諤方程)的局限性,並探討自鏇的相對論起源。 第14章:原子結構精細化: 應用前麵學到的所有工具,精確分析氫原子能級結構,包括精細結構(相對論修正)和超精細結構(自鏇-軌道耦閤)。 第15章:固體中的量子理論簡介: 將量子概念應用於凝聚態物理的初步問題,例如晶格振動(聲子)和電子的能帶理論的半經典圖像。 教材的教學哲學: 本書的設計宗旨在於平衡“物理圖像”與“數學嚴謹性”。作者認為,真正的物理理解來自於對數學結構的深刻把握。因此,每引入一個新概念,都會伴隨著詳盡的數學推導,隨後通過經典實例(如氫原子、諧振子)進行物理意義的鞏固。習題設計具有梯度性,從基礎計算到概念辨析,再到需要綜閤運用多章知識的挑戰性問題,全麵檢驗讀者的掌握程度。本書尤其強調對測量過程的哲學探討,引導學生批判性地看待量子力學的解釋問題。 --- (此簡介旨在全麵描述一本關於量子力學的經典教材,其內容完全避開瞭宇宙學、廣義相對論、標準模型、早期宇宙演化等與《宇宙學的物理基礎》直接相關的主題。)