The thermodynamics of quantum Yang-Mills theory: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVIII, 461 S. graph. Darst. |
| ISBN: | 9814329045 9789814329040 |
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| 245 | 1 | 0 | |a The thermodynamics of quantum Yang-Mills theory |b theory and applications |c Ralf Hofmann |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2012 | |
| 300 | |a XVIII, 461 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804148938622631936 |
|---|---|
| adam_text | Titel: The thermodynamics of quantum Yang-Mills theory
Autor: Hofmann, Ralf
Jahr: 2012
Contents
Preface vii
Part 1 Theory 1
1. The Classical Yang-Mills Action 3
1.1 Historic Remarks..................... 3
1.2 The Semisimple Lie Group SU(N) (N 2)....... 6
1.3 Gauge Connection AM and its Field Strength F µv ... 10
1.4 Gauge-Invariant Objects................. 12
1.4.1 Action density and energy-momentum tensor 12
1.4.2 Nonlocal objects................ 16
1.5 Spontaneous Gauge-Symmetry Breaking ....... 17
1.6 Homotopy Groups: Concept and Use.......... 19
References............................. 23
2. The Perturbative Approach at Zero Temperature 25
2.1 General Remarks..................... 25
2.2 Gauge Fixing in the Functional Integration...... 27
2.3 One-loop Running of the Gauge Coupling....... 32
2.3.1 Feynman rules................. 32
2.3.2 Callan-Symanzik equation.......... 33
2.3.3 Computation of the B function........ 34
References............................. 41
3. Aspects of Finite-Temperature Field Theory 43
3.1 Free-Particle Partition Function: Real Scalar Field ... 43
3.1.1 Euclidean formulation of thermal
field theory................... 44
3.1.2 Rotation to real time............ 50
3.2 Perturbative Loop Expansion in Thermal Gauge Theory 55
3.3 Electric Center Symmetry................ 59
3.3.1 Polyakov loop: Definition........... 60
3.3.2 Polyakov loop as an order parameter .... 61
References............................. 64
4. Selfdual Field Configurations 67
4.1 The BPST Instanton and Multiinstanton
Generalization....................... 69
4.1.1 Chern-Simons current and Bogomoln yi
decomposition................. 70
4.1.2 Instanton in regular gauge.......... 72
4.1.3 Singular gauge and multiinstantons..... 74
4.2 Sketch of the ADHM-Nahm Construction....... 77
4.2.1 All charge-fc instantons on R4......... 78
4.2.2 The t Hooft-Polyakov mpnopole...... 82
4.2.3 Nahm s duality transformation....... 88
4.3 SU(2) Calorons with k = ±1............... 91
4.3.1 Trivial holonomy................ 92
4.3.2 Nontrivial holonomy............. 94
4.4 One-loop Quantum Weights of Calorons........ 102
4.4.1 Harrington-Shepard solution........ 102
4.4.2 Lee-Lu-Kraan-van Baal solution...... 104
References............................. 109
5. The Deconfining Phase 113
5.1 Deconfining Thermal Ground State........... 114
5.1.1 Two principles imposed by infinite volume
Yang-Mills thermodynamics......... 114
5.1.2 Coarse-graining and BPS saturation..... 115
5.1.3 Inert adjoint scalar field: Phase........ 116
5.1.4 Inert adjoint scalar field: Modulus
and potential.................. 128
5.1.5 Effective action and a priori estimate
of thermal ground state............ 133
5.2 Free Thermal Quasiparticles............... 140
5.2.1 Quasiparticle spectrum, propagators,
and momentum constraints ......... 140
5.2.2 Pressure and energy density
of noninteracting excitations......... 144
5.2.3 Evolution of effective gauge coupling .... 145
5.2.4 Trace anomaly of energy-momentum
tensor...................... 149
5.2.5 Fundamental versus effective
gauge coupling................. 150
5.3 Effective Radiative Corrections............. 154
5.3.1 Loop expansion: General considerations . . 154
5.3.2 Feynman rules in unitary-Coulomb
gauge...................... 154
5.3.3 Loop expansion: Conjecture
on its termination............... 157
5.3.3.1 Pinch singularities.......... 157
5.3.3.2 Loop integration variables versus
constraints.............. 159
5.3.3.3 Two examples ............ 162
5.3.3.4 Conclusions.............. 167
5.3.4 Two-loop corrections to the pressure .... 167
5.3.4.1 General considerations....... 167
5.3.4.2 Calculation.............. 169
5.3.5 Pressure: Three-loop estimates........ 190
5.3.6 Summary: Loop expansion of pressure . . . 197
5.3.7 One-loop polarization tensor
of the massless mode............. 198
5.3.7.1 General considerations....... 198
5.3.7.2 Prerequistes.............. 198
5.3.7.3 Calculation of G for p2 = 0..... 200
5.3.7.4 Results and discussion: G at p2 = 0 204
5.3.7.5 Calculation of G at p2 = G ..... 207
5.3.7.6 Propagation of longitudinal modes 211
5.4 Stable, Screened Magnetic Monopoles......... 214
5.4.1 Remarks on screening of static
magnetic charge................ 214
5.4.2 Monopole density, monopole-antimonopole
distance, and screening length........ 219
5.4.3 Area law for spatial Wilson loop?...... 221
5.4.4 Spatial Wilson loop in effective variables . . 222
5.4.4.1 Generalities on spatial Wilson loop
in the effective theory........ 222
5.4.4.2 Part due to tree-level massive
modes................. 225
5.4.4.3 Thermal part due to massless
mode ................. 226
5.4.4.4 Quantum part due to massless
mode ................. 228
5.4.4.5 Summary of results for effective
spatial Wilson ............ 229
5.4.5 Improved ground state estimate
by thermal resummation........... 231
5.5 Thermomagnetic Effect.................. 237
5.5.1 Adiabatic approximation........... 238
5.5.2 Minkowskian Yang-Mills equations for static
fields in unitary gauge ............ 239
5.5.3 Simple static configurations with
a U(l) magnetic field ............. 240
5.5.4 Profiles..................... 242
References............................. 248
6. The Preconfining Phase 251
6.1 Condensation of Magnetic Monopole-Antimonopole
Pairs............................. 253
6.1.1 Geometric considerations........... 253
6.1.2 Derivation of the phases of macroscopic
complex scalar fields ............. 255
6.1.3 Onset of monopole condensation...... 259
6.1.4 Coarse-grained and free monopoles:
BPS saturation and Euler-Langrange .... 264
6.2 The Dual Gauge Field................... 266
6.2.1 Effective action for the preconfining phase
and thermal ground state........... 266
6.2.2 Free quasiparticle excitations, scale matching,
and running magnetic coupling....... 268
6.2.3 Supercooling.................. 272
6.3 Abrikosov-Nielsen-Olesen (ANO) Vortex Lines and
Center-Vortex Loops................... 275
6.3.1 ANO vortex in the Abelian Higgs model . . 276
References............................. 282
7. The Confining Phase 283
7.1 Decay of the Preconfining Ground State........ 284
7.1.1 The center-vortex condensate O....... 284
7.1.2 Real-time relaxation of O to zero energy
density and pressure ............. 287
7.1.3 Multiplicity of center-vortex loops with n
selfintersections................ 290
7.2 Nonthermal Pressure................... 293
7.2.1 Naive thermodynamical estimate...... 293
7.2.2 Borel resummation and analytic
continuation.................. 295
7.3 Evolving Center-Vortex Loops.............. 302
7.3.1 The case of n = 0: Mass gap ......... 303
7.3.2 The case of n = 1: Emergence of order . . . 318
References............................. 331
Part 2 Applications 333
8. The Approach of Thermal Lattice Gauge Theory 335
8.1 Pressure, Energy Density, and Entropy Density .... 337
8.2 Differential versus Integral Method:
Thermodynamical Quantities.............. 347
8.3 Analytical Aspects of Thermal
Lattice Gauge Theory................... 349
8.3.1 Identification of relevant field
configurations................. 349
8.3.2 Lattice manifestation of p and spatial
Wilson loop................... 350
8.3.3 Where is the preconfining phase?...... 352
References............................. 353
9. Black-Body Anomaly 357
9.1 Introduction........................ 357
9.2 The Cosmic Microwave Background (CMB)...... 366
9.2.1 Historical remarks and results
of CMB explorations.............. 366
9.3 SU(2)cmb and Thermal Photon Propagation...... 368
9.3.1 Modified dispersion law and spectral
energy density................. 369
9.4 Determination of Tc.................... 372
9.4.1 Very weak evidence for Tc ~ 2.73 K:
Extragalactic magnetic fields......... 372
9.4.2 Weak evidence for Tc ~ 2.73 K: Cold clouds
of dilute atomic hydrogen within the
Milky Way................... 374
9.4.3 Evidence for Tc ~ 2.73 K: CMB at very
low frequencies ................ 377
9.4.3.1 Arcade 2 and earlier radio frequency
surveys of the CMB......... 377
9.4.3.2 Evanescent CMB photons at low
frequencies.............. 378
9.4.3.3 Thermodynamical decoupling:
Coexistence of several temperatures 386
9.5 Laboratory Experiment on Black-Body Anomaly . . . 387
9.5.1 Bolometry and radiometry
of SU(2) photons................ 388
9.5.2 Preparation of a U(l) black-body cavity at low
temperatures.................. 396
9.5.3 Wave-guide loads to detect the black-body
anomaly?.................... 398
References............................. 399
10. Astrophysical and Cosmological Implications
of SU(2)cmb 403
10.1 Cold and Dilute Clouds of Atomic Hydrogen..... 403
10.1.1 Two-point correlation of energy density in
thermal U(l) gauge theory.......... 404
10.1.1.1 General strategy........... 404
10.1.1.2 Decomposition into thermal and
vacuum parts............. 406
10.1.1.3 Results................. 408
10.1.2 The case of deconfining thermal SU(2) gauge
theory...................... 412
10.1.2.1 Radiative modification of dispersion
law for massless mode ....... 413
10.1.2.2 Thermal part of two-point
correlation .............. 414
10.1.2.3 Estimate for vacuum part
of two-point correlation....... 415
10.1.2.4 Numerical results.......... 417
10.1.3 Stability of clouds of atomic hydrogen
in the Milky Way................ 418
10.2 Large-angle Anomalies of the CMB........... 420
10.2.1 Temperature as a scalar field......... 423
10.2.2 Temperature fluctuations and background
cosmology................... 424
10.2.3 Dynamic component in the cosmic dipole:
Numerical analysis .............. 428
10.2.3.1 Principle remarks and boundary
conditions............... 428
10.2.3.2 Results................. 434
10.2.4 Alignment and suppression of low
multipoles?................... 436
10.3 Planck-scale Axion and Dark Energy.......... 437
10.3.1 Model of the very early universe....... 437
10.3.2 Planck-scale axion: Cosmological evolution
after CMB decoupling............. 439
10.3.2.1 Cosmological evolution from
zdec = 1089 to z = 0......... 440
10.3.2.2 Massive CMB photons
in the future.............. 445
10.3.2.3 Slowly rolling Planck-scale axion:
Dark energy and dark matter? . . . 447
References............................. 448
Acknowledgments 451
Author Index 453
Subject Index 457
|
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| language | English |
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| physical | XVIII, 461 S. graph. Darst. |
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| publisher | World Scientific |
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| spelling | Hofmann, Ralf 1971- Verfasser (DE-588)1093622393 aut The thermodynamics of quantum Yang-Mills theory theory and applications Ralf Hofmann New Jersey [u.a.] World Scientific 2012 XVIII, 461 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Yang-Mills-Theorie (DE-588)4190409-6 gnd rswk-swf Yang-Mills-Theorie (DE-588)4190409-6 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024820726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hofmann, Ralf 1971- The thermodynamics of quantum Yang-Mills theory theory and applications Quantenfeldtheorie (DE-588)4047984-5 gnd Yang-Mills-Theorie (DE-588)4190409-6 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4190409-6 |
| title | The thermodynamics of quantum Yang-Mills theory theory and applications |
| title_auth | The thermodynamics of quantum Yang-Mills theory theory and applications |
| title_exact_search | The thermodynamics of quantum Yang-Mills theory theory and applications |
| title_full | The thermodynamics of quantum Yang-Mills theory theory and applications Ralf Hofmann |
| title_fullStr | The thermodynamics of quantum Yang-Mills theory theory and applications Ralf Hofmann |
| title_full_unstemmed | The thermodynamics of quantum Yang-Mills theory theory and applications Ralf Hofmann |
| title_short | The thermodynamics of quantum Yang-Mills theory |
| title_sort | the thermodynamics of quantum yang mills theory theory and applications |
| title_sub | theory and applications |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Yang-Mills-Theorie (DE-588)4190409-6 gnd |
| topic_facet | Quantenfeldtheorie Yang-Mills-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024820726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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