Quantum field theory: from operators to path integrals
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2010
|
| Edition: | 2., rev., and enlarged ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIV, 424 S. Ill., graph. Darst. |
| ISBN: | 9783527408467 |
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Record in the Search Index
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IMAGE 1
VII
CONTENTS
PREFACE XIII
1 INTRODUCING QUANTUM FIELDS 1 1.1 THE CLASSICAL STRING 1 1.2
RENORMALIZATION 5 1.3 THE QUANTUM STRING 5
1.4 SECOND QUANTIZATION 6 1.5 CREATION AND ANNIHILATION OPERATORS 1.6
BOSE AND FERMI STATISTICS 11
2 SCALAR FIELDS 17
2.1 KLEIN-GORDON EQUATION 17 2.2 REAL SCALAR FIELD 18
2.3 ENERGY AND MOMENTUM 19 2.4 PARTICLE SPECTRUM 21 2.5 CONTINUUM
NORMALIZATION 22 2.6 COMPLEX SCALAR FIELD 23
2.7 CHARGE AND ANTIPARTIDE 25 2.8 MICROCAUSALITY 26 2.9 THE FEYNMAN
PROPAGATOR 27 2.10 THE WAVE FUNCTIONAL 29 2.11 FUNCTIONAL OPERATIONS 30
2.12 VACUUM WAVE FUNCTIONAL 32 2.13 THE 0 4 THEORY 34
3 RELATIVISTIC FIELDS 39
3.1 LORENTZ TRANSFORMATIONS 39 3.2 MINIMAL REPRESENTATION: SL(2C) 41 3.3
THE POINCARE GROUP 43 3.4 SCALAR, VECTOR, AND SPINOR FIELDS 45 3.5
RELATIVISTIC QUANTUM FIELDS 47 3.6 ONE-PARTICLE STATES 48
4 CANONICAL FORMALISM 55
4.1 PRINCIPLE OF STATIONARY ACTION 55
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/998577847
DIGITALISIERT DURCH
IMAGE 2
VILI I CONTENTS
4.2 NOETHER'S THEOREM 57
4.3 TRANSLATIONAL INVARIANCE 58 4.4 LORENTZ INVARIANCE 61 4.5
SYMMETRIZED ENERGY-MOMENTUM TENSOR 63 4.6 GAUGE INVARIANCE 65
5 ELECTROMAGNETIC FIELD 69 5.1 MAXWELL'S EQUATIONS 69 5.2 COVARIANCE OF
THE CLASSICAL THEORY 71 5.3 CANONICAL FORMALISM 73
5.4 QUANTIZATION IN COULOMB GAUGE 75 5.5 SPIN ANGULAR MOMENTUM 78 5.6
INTRINSIC PARITY 79
5.7 TRANSVERSE PROPAGATOR 81 5.8 VACUUM FLUCTUATIONS 82 5.9 THE CASIMIR
EFFECT 84 5.10 THE GAUGE PRINCIPLE 88
6 DIRAC EQUATION 95
6.1 DIRAC ALGEBRA 95 6.2 WAVE FUNCTIONS AND CURRENT DENSITY 98 6.3 PLANE
WAVES 99
6.4 LORENTZ TRANSFORMATIONS 102 6.5 INTERPRETATION OF DIRAC MATRICES 105
6.6 EXTERNAL ELECTROMAGNETIC FIELD 106 6.7 NON-RELATIVISTIC LIMIT 108
6.8 THOMAS PRECESSION 110 6.9 HOLE THEORY 112
6.10 CHARGE CONJUGATION 115 6.11 MASSLESS PARTICLES 116
7 THE DIRAC FIELD 123 7.1 QUANTIZATION OF THE DIRAC FIELD 123 7.2
FEYNMAN PROPAGATOR 126 7.3 NORMAL ORDERING 128
7.4 ELECTROMAGNETIC INTERACTIONS 128 7.5 ISOSPIN 129
7.6 PARITY 131
7.7 CHARGE CONJUGATION 132 7.8 TIME REVERSAL 133
8 DYNAMICS OF INTERACTING FIELDS 239 8.1 TIME EVOLUTION 139 8.2
INTERACTION PICTURE 140 8.3 ADIABATIC SWITCHING 142
8.4 CORRELATION FUNCTIONS IN THE INTERACTION PICTURE 145 8.5 S-MATRIX
AND SCATTERING 147
IMAGE 3
CONTENTS IIX
8.6 SCATTERING CROSS SECTION 148
8.7 POTENTIAL SCATTERING 151 8.8 ADIABATIC THEOREM 154
9 FEYNMAN GRAPHS 359
9.1 PERTURBATION THEORY 159 9.2 TIME-ORDERED AND NORMAL PRODUCTS 160 9.3
WICK'S THEOREM 161 9.4 FEYNMAN RULES FOR SCALAR THEORY 164
9.5 TYPES OF FEYNMAN GRAPHS 369 9.5.1 VACUUM GRAPH 169 9.5.2 SELF-ENERGY
GRAPH 170 9.5.3 CONNECTED GRAPH 170 9.6 WICK ROTATION 173 9.7
REGULARIZATION SCHEMES 172 9.8 LINKED-CLUSTER THEOREM 173
9.9 VACUUM GRAPHS 374
10 VACUUM CORRELATION FUNCTIONS 181 10.1 FEYNMAN RULES 183 10.2
REDUCTION FORMULA 184 10.3 THE GENERATING FUNCTIONAL 387 10.4 CONNECTED
CORRELATION FUNCTIONS 188 10.5 LEHMANN REPRESENTATION 389 10.6
DYSON-SCHWINGER EQUATIONS 392 10.7 BOUND STATES 395 10.8 BETHE-SALPETER
EQUATION 198
11 QUANTUM ELECTRODYNAMICS 203 11.1 INTERACTION HAMILTONIAN 203 11.2
PHOTON PROPAGATOR 205 11.3 FEYNMAN GRAPHS 209
11.4 FEYNMAN RULES 234 11.5 PROPERTIES OF FEYNMAN GRAPHS 235
12 PROCESSES IN QUANTUM ELECTRODYNAMICS 219 12.1 COMPTON SCATTERING 239
12.2 ELECTROMAGNETIC FORM FACTORS 223 12.3 ANOMALOUS MAGNETIC MOMENT 227
12.4 CHARGE DISTRIBUTION 230
13 PERTURBATIVE RENORMALIZATION 235 13.1 PRIMITIVE DIVERGENCES IN QED
235 13.2 ELECTRON SELF-ENERGY 237 13.3 VACUUM POLARIZATION 241
13.4 RUNNING COUPLING CONSTANT 244 13.5 FULL VERTEX 245
IMAGE 4
X I CONTENTS
13.6 WARD IDENTITY 246
13.7 RENORMALIZATION TO SECOND ORDER 248 13.8 RENORMALIZATION TO ALL
ORDERS 249 13.9 CALLAN-SYMANZIK EQUATION 253 13.10 TRIVIALITY 255
14 PATH INTEGRALS 263 14.1 PATH INTEGRALS IN QUANTUM MECHANICS 263 14.2
TIME-ORDERING 264 14.3 IMAGINARY TIME 265
14.4 PATH INTEGRALS IN QUANTUM FIELD THEORY 266 14.5 EUCLIDEAN
SPACE-TIME 267 14.6 VACUUM AMPLITUDES 268 14.7 STATISTICAL MECHANICS 271
14.8 GAUSSIAN INTEGRALS 273
14.9 PERTURBATION THEORY 276 14.10 THE LOOP EXPANSION 279 14.11 BOSON
AND FERMION LOOPS 280 14.12 GRASSMANN VARIABLES 282
15 BROKEN SYMMETRY 291 15.1 WHY BROKEN SYMMETRY 291 15.2 FERROMAGNETISM
294 15.3 SPIN WAVES 296
15.4 BREAKING GAUGE INVARIANCE 299 15.5 SUPERFLUIDITY 302 15.6
GINSBURG-LANDAU THEORY 305 15.7 EFFECTIVE ACTION 307
15.8 EFFECTIVE POTENTIAL 308
16 RENORMALIZATION 315 16.1 THE CUTOFF AS SCALE PARAMETER 315 16.2 RG
TRAJECTORIES 318 16.3 FIXED POINTS 319
16.4 MOMENTUM SPACE RG 320 16.5 REAL SPACE RG 322 16.6 RENORMALIZATION
OF CORRELATION FUNCTIONS 325 16.7 RELEVANT AND IRRELEVANT PARAMETERS 326
16.8 THE FREE FIELD 327 16.9 IR FIXED POINT AND PHASE TRANSITION 329
16.10 CROSSOVER 330 16.11 PERTURBATIVE RENORMALIZATION REVISITED 331
16.12 CRITICAL EVALUATION 332 16.13 WHY CORRECT THEORIES ARE BEAUTIFUL
333
17 THE GAUSSIAN FIXED POINT 339 17.1 STABILITY OF THE FREE FIELD 339
IMAGE 5
CONTENTS I XI
17.2 GENERAL SCALAR FIELD 340
17.3 FEYNMAN GRAPHS 341 17.4 WEGNER-HOUGHTON EQUATION 343 17.5
RENORMALIZED COUPLINGS 346 17.6 THE RG MATRIX 348 17.7 NON-TRIVIALITY
AND ASYMPTOTIC FREEDOM 353 17.8 THE CASE D = 2 353
18 IN TWO DIMENSIONS 357 18.1 ABSENCE OF LONG-RANGE ORDER 357 18.2
TOPOLOGICAL ORDER 358 18.3 XY MODEL 360 18.4 KOSTERLITZ-THOULESS
TRANSITION 364 18.5 VORTEX MODEL 364 18.6 2D SUPERFLUIDITY 366 18.7 RG
TRAJECTORIES 368 18.8 UNIVERSAL JUMP OF SUPERFLUID DENSITY 372
19 TOPOLOGICAL EXCITATIONS 375 19.1 TOPOLOGICAL SOLITON 375 19.2
INSTANTON AND TUNNELING 378 19.3 DEPINNING OF CHARGE DENSITY WAVES 379
19.4 NONLINEAR SIGMA MODEL 383 19.5 THE SKYRMION 385 19.6 THE HOPF
INVARIANT 389 19.7 FRACTIONAL SPIN 391
19.8 MONOPOLES, VORTICES, AND ANOMALIES 393
APPENDIX A BACKGROUND MATERIAL 399 A.I NOTATION 399
A.2 CLASSICAL MECHANICS 400 A.3 QUANTUM MECHANICS 401
APPENDIX B SUPERFLUIDITY 405 B.I LINEAR RESPONSE 405 B.2 NORMAL FLUID
AND SUPERFLUID 406 B.3 SUPERFLUID DENSITY 408
APPENDIX C POLCHINSKI'S RENORMALIZATION EQUATION 43 3 C.I
RENORMALIZATION SCHEME 433 C.2 THE EQUATION 432
C.3 ASYMPTOTICALLY FREE SCALAR FIELD 414
INDEX 417 |
| any_adam_object | 1 |
| author | Huang, Kerson 1928-2016 |
| author_GND | (DE-588)132848201 |
| author_facet | Huang, Kerson 1928-2016 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2., rev., and enlarged ed. |
| format | Book |
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| spelling | Huang, Kerson 1928-2016 Verfasser (DE-588)132848201 aut Quantum field theory from operators to path integrals Kerson Huang 2., rev., and enlarged ed. Weinheim Wiley-VCH 2010 XIV, 424 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenfeldtheorie (DE-588)4047984-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3385127&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019010142&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huang, Kerson 1928-2016 Quantum field theory from operators to path integrals Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4123623-3 |
| title | Quantum field theory from operators to path integrals |
| title_auth | Quantum field theory from operators to path integrals |
| title_exact_search | Quantum field theory from operators to path integrals |
| title_full | Quantum field theory from operators to path integrals Kerson Huang |
| title_fullStr | Quantum field theory from operators to path integrals Kerson Huang |
| title_full_unstemmed | Quantum field theory from operators to path integrals Kerson Huang |
| title_short | Quantum field theory |
| title_sort | quantum field theory from operators to path integrals |
| title_sub | from operators to path integrals |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantenfeldtheorie Lehrbuch |
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