A unified grand tour of theoretical physics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2013
|
| Edition: | Third Edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index Hier auch später erschienen, unveränderte Nachdrucke |
| Physical Description: | xix, 693 S. graph. Darst. |
| ISBN: | 9781439884461 9781138473355 |
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| 245 | 1 | 0 | |a A unified grand tour of theoretical physics |c Ian D. Lawrie |
| 250 | |a Third Edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2013 | |
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| adam_text | Titel: A unified grand tour of theoretical physics
Autor: Lawrie, Ian D
Jahr: 2013
Contents
Preface xi
Preface to the First Edition xiii
Preface to the Second Edition xv
Glossary of Mathematical Symbols xvii
1 Introduction: The Ways of Nature 1
2 Geometry 5
2.0 The Special and General Theories of Relativity ....... 6
2.0.1 The Special Theory................... 6
2.0.2 The General Theory .................. 11
2.1 Spacetime as a Differentiable Manifold............ 14
2.1.1 Topology of the Real Line «. and of Rd......... 16
2.1.2 Differentiable Spacetime Manifold........... 18
2.1.3 Summary and Examples................ 20
2.2 Tensors ............................. 22
2.3 Extra Geometrical Structures ................. 27
2.3.1 The Affine Connection................. 28
2.3.2 Geodesies ........................ 33
2.3.3 The Riemann Curvature Tensor............ 34
2.3.4 The Metric........................ 36
2.3.5 The Metric Connection................. 38
2.4 What Is the Structure of Our Spacetime? .......... 39
3 Classical Physics in Galilean and Minkowski Spacetimes 45
3.1 The Action Principle in Galilean Spacetime ......... 46
3.2 Symmetries and Conservation Laws ............. 50
3.3 The Hamiltonian ........................ 52
3.4 Poisson Brackets and Translation Operators......... 53
3.5 The Action Principle in Minkowski Spacetime........ 56
3.6 Classical Electrodynamics ................... 61
3.7 *Geometry in Classical Physics ................ 64
3.7.1 More on Tensors .................... 65
vi Contents
3.7.2 Differential Forms, Dual Tensors and Maxwell s Equa-
tions ........................... 67
3.7.3 Configuration Space and Its Relatives......... 73
3.7.4 The Symplectic Geometry of Phase Space...... 75
3.8 *Hamiltonian Dynamics of Constrained Systems ...... 79
3.8.1 A System with Second-Class Constraints....... 80
3.8.2 A System with a First-Class Constraint........ 87
3.8.3 General Constrained Systems............. 91
4 General Relativity and Gravitation 97
4.1 The Principle of Equivalence ................. 97
4.2 Gravitational Forces ...................... 98
4.3 The Field Equations of General Relativity.......... 102
4.4 The Gravitational Field of a Spherical Body......... 106
4.4.1 The Schwarzschild Solution .............. 106
4.4.2 Time Near a Massive Spherical Body......... 108
4.4.3 Distances Near a Massive Spherical Body ...... 110
4.4.4 Particle Trajectories Near a Massive Spherical Body 111
4.5 Black Holes ........................... 112
4.5.1 Schwarzschild Black Holes............... 113
4.5.2 *Mass and Surface Gravity of a Schwarzschild Black
Hole........................... 119
4.5.3 *Rotating Black Holes and Black-Hole Thermodynam-
ics ............................ 124
5 Quantum Theory 141
5.0 Wave Mechanics ........................ 142
5.1 The Hilbert Space of State Vectors.............. 145
5.2 Operators and Observable Quantities............. 148
5.3 Spacetime Translations and the Properties of Operators . . 151
5.4 Quantization of a Classical System.............. 155
5.5 An Example: The One-Dimensional Harmonic Oscillator . . 157
6 Second Quantization and Quantum Field Theory 165
6.1 The Occupation-Number Representation........... 166
6.2 Field Operators and Observables ............... 169
6.3 Lagrangian Formalism for Field Operators.......... 171
6.4 Second Quantization for Fermions .............. 173
7 Relativistic Wave Equations and Field Theories 177
7.1 The Klein-Gordon Equation ................. 178
7.2 Scalar Field Theory for Free Particles ............ 181
7.3 The Dirac Equation and Spin-| Particles .......... 183
7.3.1 The Dirac Equation................... 183
7.3.2 Lorentz Covariance and Spin.............. 185
7.3.3 Some Properties of the 7 Matrices........... 189
Contents vii
7.3.4 Conjugate Wavefunction and the Dirac Action .... 190
7.3.5 Probability Current and Bilinear Covariants..... 190
7.3.6 Plane-Wave Solutions.................. 192
7.3.7 Massless Spin-^ Particles................ 193
7.4 Spinor Field Theory ...................... 194
7.5 Weyl and Majorana Spinors.................. 197
7.6 Particles of Spin 1 and 2.................... 202
7.6.1 Photons and Massive Spin-1 Particles......... 203
7.6.2 Gravitons ........................ 205
7.7 Wave Equations in Curved Spacetime ............ 208
8 Forces, Connections and Gauge Fields 221
8.1 Electromagnetism ....................... 221
8.2 Non-Abelian Gauge Theories ................. 227
8.3 Non-Abelian Theories and Electromagnetism ........ 234
8.4 Relevance of Non-Abelian Theories to Physics........ 235
8.5 The Theory of Kaluza and Klein ............... 236
9 Interacting Relativistic Field Theories 241
9.1 Asymptotic States and the Scattering Operator....... 242
9.2 Reduction Formulae ...................... 244
9.3 Path Integrals.......................... 247
9.3.1 Path Integrals in Non-Relativistic Quantum Mechanics 247
9.3.2 Functional Integrals in Quantum Field Theory .... 250
9.4 Perturbation Theory...................... 253
9.5 Quantization of Gauge Fields ................. 257
9.6 Renormalization ........................ 260
9.7 Quantum Electrodynamics .................. 266
9.7.1 The Coulomb Potential................. 266
9.7.2 Vacuum Polarization.................. 269
9.7.3 The Lamb Shift..................... 271
9.7.4 The Running Coupling Constant ........... 272
9.7.5 Anomalous Magnetic Moments ............ 273
10 Equilibrium Statistical Mechanics 279
10.1 Ergodic Theory and the Microcanonical Ensemble ..... 280
10.2 The Canonical Ensemble.................... 285
10.3 The Grand Canonical Ensemble................ 287
10.4 Relation between Statistical Mechanics and Thermodynamics 289
10.5 Quantum Statistical Mechanics ................ 295
10.6 Field Theories at Finite Temperature ............ 299
10.7 Black-Body Radiation ..................... 302
10.8 The Classical Lattice Gas ................... 304
10.9 Analogies between Field Theory and Statistical Mechanics . 306
viii Contents
11 Phase Transitions 311
11.1 Bose-Einstein Condensation.................. 311
11.2 Critical Points in Fluids and Magnets ............ 313
11.3 The Ising Model ........................ 319
11.4 Spontaneous Symmetry Breaking............... 321
11.5 The Ginzburg-Landau Theory ................ 324
11.6 The Renormalization Group.................. 327
11.7 The Ginzburg-Landau Theory of Superconductors ..... 333
11.7.1 Spontaneous Breaking of Continuous Symmetries . . 333
11.7.2 Magnetic Effects in Superconductors......... 335
11.7.3 The Higgs Mechanism ................. 337
12 Unified Gauge Theories of the Fundamental Interactions 341
12.1 The Weak Interaction ..................... 342
12.2 The Glashow-Weinberg-Salam Model for Leptons ..... 347
12.3 Physical Implications of the Model for Leptons ....... 352
12.4 Hadronic Particles in the Electroweak Theory........ 354
12.4.1 Quarks.......................... 354
12.4.2 Quarks in the Electroweak Theory .......... 358
12.5 Colour and Quantum Chromodynamics ........... 360
12.6 Loose Ends ........................... 366
12.6.1 The Higgs Boson.................... 366
12.6.2 Massive Neutrinos.................... 369
12.7 Grand Unified Theories .................... 373
12.8 *Supersymmetry ........................ 381
12.8.1 The Wess-Zumino Model................ 382
12.8.2 Superfields........................ 383
12.8.3 Spontaneous Supersymmetry Breaking........ 385
12.8.4 The Supersymmetry Algebra.............. 388
12.8.5 Supersymmetric Gauge Theories and Supergravity . 393
12.8.6 Some Algebraic Details................. 397
13 Solitons and So On 401
13.1 Domain Walls and Kinks ................... 401
13.2 The Sine-Gordon Solitons................... 410
13.3 Vortices and Strings ...................... 414
13.4 Magnetic Monopoles ...................... 424
14 The Early Universe 435
14.1 The Robertson-Walker Metric ................ 436
14.2 The Friedmann-Lemaitre Models............... 441
14.3 Matter, Energy and the Age of the Universe......... 445
14.4 The Fairly Early Universe................... 450
14.5 Nucleosynthesis......................... 458
14.6 Recombination and the Horizon Problem .......... 461
Contents ix
14.7 The Flatness Problem ..................... 463
14.8 Density Perturbations ..................... 464
14.8.1 Field Equations for Linear Perturbations....... 465
14.8.2 Perturbations of Ideal Fluids.............. 467
14.8.3 Adiabatic Perturbations................ 469
14.8.4 Qualitative Features of the CMBR Anisotropies . . . 470
14.9 The Very Early Universe.................... 475
14.9.1 Cosmological Phase Transitions............ 476
14.9.2 Inflation......................... 479
14.9.3 Density Perturbations Generated during Inflation . . 486
14.10 Dark Energy and Dark Matter ................ 493
15 *An Introduction to String Theory 499
15.1 The Relativistic Point Particle ................ 501
15.2 The Free Classical String ................... 505
15.2.1 The String Action.................... 505
15.2.2 Weyl Invariance and Gauge Fixing.......... 509
15.2.3 The Euclidean Worldsheet and Conformal Invariance 511
15.2.4 Mode Expansions.................... 515
15.2.5 A Useful Transformation................ 520
15.3 Quantization of the Free Bosonic String ........... 522
15.3.1 The Quantum Virasoro Algebra............ 523
15.3.2 Quantum Gauge Fixing................. 529
15.3.3 The Critical Spacetime Dimension........... 533
15.3.4 The Ghost Hilbert Space................ 537
15.3.5 The BRST Cohomology ................ 539
15.4 Physics of the Free Bosonic String .............. 544
15.4.1 The Mass Spectrum................... 544
15.4.2 Vertex Operators.................... 549
15.4.3 Strings and Quantum Gravity............. 552
15.5 Further Developments ..................... 555
15.5.1 String Interactions ................... 555
15.5.2 Superstrings....................... 559
15.5.3 The Ramifications of Compactification........ 561
15.5.4 Large Extra Dimensions................ 568
16 *Gravity and Quantum Mechanics 575
16.1 Canonical Quantization of General Relativity ........ 575
16.1.1 Hamiltonian Formulation of General Relativity . . . 576
16.1.2 New Variables: Triads, Holonomies and Fluxes .... 586
16.1.3 Towards a Quantum Theory of Gravity........ 596
16.2 Quantum Cosmology...................... 608
16.2.1 The Problem of Time.................. 609
16.2.2 Loop Quantum Cosmology............... 614
16.3 Black-Hole Entropy ...................... 617
x Contents
Some Snapshots of the Tour 623
A Some Mathematical Notes 641
A.l Delta Functions and Functional Differentiation ....... 641
A.2 The Levi-Civita Tensor Density................ 643
A.3 Vector Spaces and Hilbert Spaces............... 644
A.4 Gauss Theorem ........................ 646
A.5 Surface Area and Volume of a d-Dimensional Sphere .... 647
A.6 Gaussian Integrals ....................... 648
A.7 Grassmann Variables...................... 649
B Some Elements of Group Theory 651
C Natural Units 665
D Scattering Cross Sections and Particle Decay Rates 669
Bibliography 673
References 677
Index 685
|
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| spelling | Lawrie, Ian D. Verfasser aut A unified grand tour of theoretical physics Ian D. Lawrie Third Edition Boca Raton ; London ; New York CRC Press 2013 xix, 693 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Hier auch später erschienen, unveränderte Nachdrucke Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Theoretische Physik (DE-588)4117202-4 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Theoretische Physik (DE-588)4117202-4 s DE-604 Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025742601&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lawrie, Ian D. A unified grand tour of theoretical physics Mathematische Physik (DE-588)4037952-8 gnd Theoretische Physik (DE-588)4117202-4 gnd |
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| title | A unified grand tour of theoretical physics |
| title_auth | A unified grand tour of theoretical physics |
| title_exact_search | A unified grand tour of theoretical physics |
| title_full | A unified grand tour of theoretical physics Ian D. Lawrie |
| title_fullStr | A unified grand tour of theoretical physics Ian D. Lawrie |
| title_full_unstemmed | A unified grand tour of theoretical physics Ian D. Lawrie |
| title_short | A unified grand tour of theoretical physics |
| title_sort | a unified grand tour of theoretical physics |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Theoretische Physik (DE-588)4117202-4 gnd |
| topic_facet | Mathematische Physik Theoretische Physik Aufgabensammlung |
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