Many-body problems and quantum field theory: an introduction ; with 7 tables and 23 exercises
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Texts and monographs in physics
Physics and astronomy online library |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013037157&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XV, 435 S. Ill. |
| ISBN: | 3540213201 |
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| 245 | 1 | 0 | |a Many-body problems and quantum field theory |b an introduction ; with 7 tables and 23 exercises |c Philippe A. Martin ; François Rothen |
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Record in the Search Index
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| adam_text | PHILIPPE A. MARTIN FRANCOIS ROTHEN MANY-BODY PROBLEMS AND QUANTUM FIELD
THEORY AN INTRODUCTION TRANSLATED BY STEVEN GOLDFARB, ANDREW JORDAN AND
SAMUEL LEACH SECOND EDITION WITH 102 FIGURES, 7 TABLES AND 23 EXERCISES
SPRINGER TABLE OF CONTENTS 1. CLASSICAL FIELDS AND THEIR ASSOCIATED
PARTICLES 3 1.1 INTRODUCTION 3 1.2 THE QUANTUM HARMONIC OSCILLATOR 5
1.2.1 REVIEW OF PROPERTIES 5 1.2.2 COHERENT STATES 9 1.2.3 THE FORCED
OSCILLATOR 14 1.2.4 NORMAL ORDERING 16 1.3 THE ELECTROMAGNETIC FIELD AND
THE PHOTON 18 1.3.1 MAXWELL S EQUATIONS 18 1.3.2 GAUGE TRANSFORMATIONS
19 1.3.3 DECOMPOSITION OF THE FIELD INTO LONGITUDINAL AND TRANSVERSE
COMPONENTS 22 1.3.4 HAMILTONIAN OF THE INTERACTION OF RADIATION WITH
NON-RELATIVISTIC MATTER 23 1.3.5 FOURIER ANALYSIS OF THE CLASSICAL FREE
FIELD 25 1.3.6 PHOTONS AND ELECTROMAGNETIC WAVES 29 1.4 THE ELASTIC
FIELD AND THE PHONON 33 1.4.1 ELASTIC WAVES AND ELASTIC ENERGY 33 1.4.2
ELASTIC WAVES AND ENERGY OF AN ISOTROPIC SOLID 36 1.4.3 FOURIER ANALYSIS
OF ELASTIC WAVES 39 1.4.4 AN ENSEMBLE OF PHONONS AND CLASSICAL ELASTIC
WAVES 41 1.4.5 THE CLASSICAL LINEAR CHAIN 42 1.4.6 THE QUANTUM LINEAR
CHAIN 47 EXERCISES 49 2. FERMIONS AND BOSONS 51 2.1 THE PRINCIPLE OF
SYMMETRIZATION 51 2.1.1 IDENTICAL PARTICLES 51 2.1.2 ONE-PARTICLE STATES
52 2.1.3 PERIODIC BOUNDARY CONDITIONS AND THE THERMODYNAMIC LIMIT 54
2.1.4 N-PARTICLE STATES 58 2.1.5 SYMMETRIZATION 60 XII TABLE OF CONTENTS
2.1.6 SYMMETRY OF COMPOSITE PARTICLES 64 2.1.7 OCCUPATION NUMBER
REPRESENTATION 65 2.2 DEGENERATE GASES 68 2.2.1 THE GROUND STATE OF N
BOSONS 68 2.2.2 THE GROUND STATE OF N FERMIONS 74 2.2.3 STABILITY OF
MATTER 79 2.2.4 NUCLEO-ELECTRONIC PLASMA AT HIGH DENSITY 82 2.2.5
FERMIONS AND GRAVITATION 83 EXERCISES 86 3. SYSTEMS WITH VARIABLE
PARTICLE NUMBER 89 3.1 INTRODUCTION 89 3.2 FORMALISM OF THE SECOND
QUANTIZATION 90 3.2.1 FOCK SPACE 90 3.2.2 CREATION AND ANNIHILATION
OPERATORS 92 3.2.3 STATES OF THE FOCK SPACE 96 3.2.4 NORMAL ORDER 99
3.2.5 ONE-BODY OPERATORS 101 3.2.6 FREE EVOLUTION AND SYMMETRIES 104
3.2.7 TWO-BODY OPERATORS 108 3.2.8 REDUCED DENSITY MATRICES AND
CORRELATIONS 113 3.2.9 CORRELATIONS IN FREE FERMI AND BOSE GASES 118 3.3
QUANTUM PHYSICS AND THE CONCEPT OF A PERFECT GAS 121 EXERCISES 123 4.
ELECTRON GAS 12 7 4.1 THE HARTREE-FOCK METHOD 127 4.1.1 THE VARIATIONAL
PRINCIPLE 127 4.1.2 THE HARTREE-FOCK EQUATIONS 129 4.2 ELECTRON GAS IN
THE HARTREE-FOCK APPROXIMATION 133 4.2.1 ELECTRON GAS AND ITS
HAMILTONIAN 133 4.2.2 THE HARTREE-FOCK ENERGY 137 4.3 THE DIELECTRIC
FUNCTION 141 4.3.1 SCREENING AND THE PLASMON 141 4.3.2 RESPONSE TO AN
EXTERNAL CHARGE 145 4.3.3 EVOLUTION OF A CHARGE FLUCTUATION 148 4.3.4
THE RPA DIELECTRIC FUNCTION 152 EXERCISES 156 5. FERMION PAIRING AND
SUPERCONDUCTIVITY 159 5.1 DOES THERE EXIST AN ANALOGUE OF THE BOSE
CONDENSATION FOR FERMIONS? 159 5.2 THE PHENOMENOLOGY OF
SUPERCONDUCTIVITY 161 5.2.1 EXPERIMENTAL FACTS 161 5.2.2 THE
PHENOMENOLOGICAL APPROACH 163 TABLE OF CONTENTS XIII 5.2.3 MACROSCOPIC
QUANTUM FLUIDS 166 5.2.4 EXISTENCE OF THE ENERGY GAP 171 5.3 BCS THEORY
172 5.3.1 THE EFFECTIVE INTERACTION BETWEEN ELECTRONS 172 5.3.2
APPLICATION OF THE VARIATIONAL METHOD TO SUPERCONDUCTIVITY 173 5.3.3
SIGN AMBIGUITY 176 5.3.4 VARIATIONAL CLASS OF BCS STATES 177 5.3.5 HOW
TO CALCULATE WITH A BCS STATE 179 5.3.6 SEARCH FOR A MINIMUM-ENERGY
STATE 183 5.3.7 THE ENERGY GAP 187 5.3.8 SPATIAL EXTENSION OF A COOPER
PAIR 189 5.4 PARTICLE NUMBER AND PHASE IN SUPERCONDUCTIVITY 191 5.4.1 IS
IT NECESSARY TO FIX THE PARTICLE NUMBER OR THE PHASE? 191 5.4.2 ANALOGY
WITH STATISTICAL PHYSICS 193 5.5 HIGH-R C SUPERCONDUCTIVITY 194
EXERCISES 196 6. NUCLEON PAIRING AND THE STRUCTURE OF THE NUCLEUS 199
6.1 INTRODUCTION 199 6.2 A BROAD OUTLINE OF THE NUCLEAR STRUCTURE 200
6.2.1 THE SHORT RANGE OF NUCLEAR FORCES 200 6.2.2 THE LIQUID DROP MODEL
200 6.2.3 MORE ABOUT NUCLEAR FORCES 203 6.3 THE SHELL MODEL OF THE
NUCLEUS 204 6.3.1 THE ONE-PARTICLE POTENTIAL INSIDE THE NUCLEUS 204
6.3.2 INTERPRETATION OF THE MAGIC NUMBERS 206 6.3.3 DISTRIBUTION OF THE
ENERGY LEVELS IN THE SHELL MODEL . 207 6.4 PAIRING OF THE NUCLEONS 209
6.4.1 NATURE OF THE RESIDUAL INTERACTION 209 6.4.2 PAIRING INTERACTION:
FURTHER EXPERIMENTAL FACTS 211 6.4.3 THE INTERACTION RESPONSIBLE FOR THE
PAIRING 214 6.4.4 APPLYING THE BCS THEORY TO THE NUCLEUS 215 6.5 WHICH
NUCLEAR PROPERTIES ARE AFFECTED BY NUCLEON PAIRING? 218 6.5.1
SUPERCONDUCTIVITY, SUPERFLUIDITY AND NUCLEI 218 6.5.2 AN EXCITED NUCLEUS
IN A ROTATIONAL STATE 221 6.5.3 MOMENT OF INERTIA OF A DEFORMED NUCLEUS
222 EXERCISES 224 TABLE OF CONTENTS THE SUPERFLUIDITY OF LIQUID HELIUM
227 7.1 EXPERIMENTAL FACTS 227 7.1.1 PHASE DIAGRAM OF |HE 227 7.1.2
PROPERTIES OF THE SUPERFLUID PHASE OF HE II 229 7.2 QUANTUM LIQUID AND
THE TWO-FLUID MODEL 231 7.2.1 THE SUPERFLUID PHASE AND QUANTUM LIQUID
231 7.2.2 DISSIPATION IN A SUPERFLUID 233 7.2.3 SECOND SOUND 238 7.3 THE
ENERGY SPECTRUM OF HE II 241 7.3.1 EXCITATIONS OF HE II 241 7.3.2
NON-VISCOUS FLOW THROUGH A CAPILLARY 245 7.4 IMPERFECT BOSE GAS 248
7.4.1 BOGOLIUBOV S APPROXIMATION AND TRANSFORMATION .... 248 7.4.2 BOSE
GAS OR LIQUID? 252 7.5 SUPERFLUIDITY OF THE LIGHT ISOTOPE 3 HE 253 7.5.1
A FERMI LIQUID 253 7.5.2 SUPERFLUIDITY OF 3 HE 254 EXERCISES 255 QUANTUM
FIELDS 257 8.1 INTRODUCTION 257 8.2 THE QUANTUM-ELECTROMAGNETIC FIELD
259 8.2.1 THE FREE FIELD 259 8.2.2 CANONICAL VARIABLES 263 8.2.3
INVARIANT COMMUTATION FUNCTION AND MICROCAUSALITY . 265 8.2.4 EMISSION
OF PHOTONS BY A CLASSICAL SOURCE 267 8.2.5 COHERENT STATES OF PHOTONS
270 8.2.6 EMISSION AND ABSORPTION OF PHOTONS BY AN ATOM .... 272 8.2.7
SPONTANEOUS EMISSION 275 8.2.8 PHOTONS AND MATTER IN EQUILIBRIUM 277
8.2.9 PHOTON STATISTICS 278 8.3 MASSIVE SCALAR FIELD 281 8.3.1 NEUTRAL
SCALAR FIELD 281 8.3.2 THE YUKAWA POTENTIAL 284 8.3.3 CHARGED SCALAR
FIELD 289 8.3.4 SPIN AND STATISTICS 295 8.3.5 THE LAGRANGIAN FORMALISM
297 8.3.6 THE GAUGE INVARIANCE PRINCIPLE AND FIELD INTERACTIONS 300
8.3.7 MASS GENERATION 305 8.4 ELECTRONS AND PHONONS 312 8.4.1
NON-RELATIVISTIC FERMI FIELD 312 8.4.2 THE QUANTUM-ELASTIC FIELD 315
8.4.3 ELECTRON-PHONON INTERACTIONS 317 EXERCISES 321 TABLE OF CONTENTS
XV 9. PERTURBATIVE METHODS IN FIELD THEORY 325 9.1 INTRODUCTION 325 9.2
THE GREEN FUNCTIONS 327 9.2.1 DEFINITION 327 9.2.2 THE FREE-PARTICLE
GREEN FUNCTION 331 9.2.3 PARTICLE IN AN EXTERNAL FIELD 334 9.2.4
SIMPLIFIED EXAMPLE: THE COOPER PAIR 340 9.3 PERTURBATIVE EXPANSION OF
THE SCATTERING OPERATOR 343 9.3.1 TIME-DEPENDENT PERTURBATION THEORY 343
9.3.2 THE SCATTERING OPERATOR 346 9.3.3 FERMIONS AND BOSONS IN
INTERACTION 350 9.3.4 THE WICK THEOREM FOR TIME-ORDERED PRODUCTS 353
9.3.5 TIME-ORDERED CONTRACTIONS AND PROPAGATORS 356 9.3.6 FEYNMAN
DIAGRAMS 360 9.4 APPLICATIONS 366 9.4.1 PHYSICAL INTERPRETATION OF THE
DIAGRAMS 366 9.4.2 ELECTROMAGNETIC INTERACTIONS: COMPTON SCATTERING . .
. 371 9.4.3 QUANTUM ELECTRODYNAMICS: RADIATIVE CORRECTIONS .... 377
9.4.4 ELECTRON-PHONON INTERACTIONS 381 9.4.5 DIAGRAM SUMMATION 384
EXERCISES 390 10. PERTURBATIVE METHODS IN MANY-BODY PROBLEMS 393 10.1
GENERAL PROPERTIES 393 10.1.1 THE ONE-BODY GREEN FUNCTION 393 10.1.2
PERTURBATIVE CALCULATION OF THE GREEN FUNCTION 397 10.1.3 PARTICLE IN AN
EXTERNAL FIELD AND THE CONNECTED-GRAPH THEOREM 402 10.1.4 INTERACTING
PARTICLES 407 10.2 APPROXIMATION SCHEMES FOR THE ELECTRON GAS 412 10.2.1
HARTREE-FOCK APPROXIMATION 412 10.2.2 RPA APPROXIMATION 414 EXERCISES
420 BIBLIOGRAPHY 423 INDEX 431
|
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| id | DE-604.BV019709768 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:04:12Z |
| institution | BVB |
| isbn | 3540213201 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013037157 |
| oclc_num | 249137062 |
| open_access_boolean | |
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| owner_facet | DE-91G DE-BY-TUM DE-703 DE-83 DE-355 DE-BY-UBR |
| physical | XV, 435 S. Ill. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics Physics and astronomy online library |
| spellingShingle | Martin, Philippe A. Rothen, François 1936- Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises Quantenfeldtheorie - Vielkörperproblem Many-body problem Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Vielkörperproblem (DE-588)4078900-7 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4078900-7 |
| title | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises |
| title_alt | Problèmes à N-corps et champs quantiques Many body problems and quantum field theory |
| title_auth | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises |
| title_exact_search | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises |
| title_full | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises Philippe A. Martin ; François Rothen |
| title_fullStr | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises Philippe A. Martin ; François Rothen |
| title_full_unstemmed | Many-body problems and quantum field theory an introduction ; with 7 tables and 23 exercises Philippe A. Martin ; François Rothen |
| title_short | Many-body problems and quantum field theory |
| title_sort | many body problems and quantum field theory an introduction with 7 tables and 23 exercises |
| title_sub | an introduction ; with 7 tables and 23 exercises |
| topic | Quantenfeldtheorie - Vielkörperproblem Many-body problem Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Vielkörperproblem (DE-588)4078900-7 gnd |
| topic_facet | Quantenfeldtheorie - Vielkörperproblem Many-body problem Quantum field theory Quantenfeldtheorie Vielkörperproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013037157&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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