| Preface to the Third Edition |
|
vii | |
| Preface to the Second Edition |
|
ix | |
| Preface to the First Edition |
|
xi | |
|
|
|
1 | (6) |
|
2. THE PATH INTEGRAL APPROACH TO QUANTIZATION |
|
|
7 | (29) |
|
2.1 The Path Integral Method in Quantum Mechanics |
|
|
8 | (7) |
|
2.2 Path Integral Representation of Bosonic Green Functions in Field Theory |
|
|
15 | (7) |
|
|
|
22 | (1) |
|
2.4 Path Integral Representation of Fermionic Green Functions |
|
|
23 | (10) |
|
2.5 Discretizing Space-Time. The Lattice as a Regulator of a Quantum Field Theory |
|
|
33 | (3) |
|
3. THE FREE SCALAR FIELD ON THE LATTICE |
|
|
36 | (7) |
|
4. FERMIONS ON THE LATTICE |
|
|
43 | (34) |
|
|
|
43 | (5) |
|
4.2 A Closer Look at Fermion Doubling |
|
|
48 | (8) |
|
|
|
56 | (1) |
|
|
|
57 | (4) |
|
4.5 Technical Details of the Staggered Fermion Formulation |
|
|
61 | (8) |
|
4.6 Staggered Fermions in Momentum Space |
|
|
69 | (4) |
|
4.7 Ginsparg-Wilson Fermions |
|
|
73 | (4) |
|
5. ABELIAN GAUGE FIELDS ON THE LATTICE AND COMPACT QED |
|
|
77 | (10) |
|
|
|
77 | (3) |
|
5.2 Lattice Formulation of QED |
|
|
80 | (7) |
|
6. NON-ABELIAN GAUGE FIELDS ON THE LATTICE COMPACT QCD |
|
|
87 | (8) |
|
7. THE WILSON LOOP AND THE STATIC QUARK-ANTIQUARK POTENTIAL |
|
|
95 | (14) |
|
7.1 A Look at Non-Relativistic Quantum Mechanics |
|
|
96 | (1) |
|
7.2 The Wilson Loop and the Static qq-Potential in QED |
|
|
97 | (8) |
|
7.3 The Wilson Loop in QCD |
|
|
105 | (4) |
|
8. THE QQ POTENTIAL IN SOME SIMPLE MODELS |
|
|
109 | (10) |
|
8.1 The Potential in Quenched QED |
|
|
109 | (5) |
|
8.2 The Potential in Quenched Compact QED2 |
|
|
114 | (5) |
|
9. THE CONTINUUM LIMIT OF LATTICE QCD |
|
|
119 | (11) |
|
9.1 Critical Behaviour of Lattice QCD and the Continuum Limit |
|
|
119 | (3) |
|
9.2 Dependece of the Coupling Constant on the Lattice Spacing and the Renormalization Group β-Function |
|
|
122 | (8) |
| 10. LATTICE SUM RULES |
|
130 | (21) |
|
10.1 Energy Sum Rule for the Harmonic Oscillator |
|
|
130 | (6) |
|
10.2 The SU(N) Gauge Action on an Anisotropic Lattice |
|
|
136 | (2) |
|
10.3 Sum Rules for the Static qq-Potential |
|
|
138 | (8) |
|
10.4 Determination of the Electric, Magnetic and Anomalous Contribution to the qq-Potential |
|
|
146 | (2) |
|
10.5 Sum Rules for the Glueball Mass |
|
|
148 | (3) |
| 11. THE STRONG COUPLING EXPANSION |
|
151 | (19) |
|
11.1 The qq-Potential to Leading Order in Strong Coupling |
|
|
151 | (3) |
|
11.2 Beyond the Leading Approximation |
|
|
154 | (4) |
|
11.3 The Lattice Hamiltonian in the Strong Coupling Limit and the String Picture of Confinement |
|
|
158 | (12) |
| 12. THE HOPPING PARAMETER EXPANSION |
|
170 | (22) |
|
12.1 Path Integral Representation of Correlation Functions in Terms of Bosonic Variables |
|
|
171 | (3) |
|
12.2 Hopping Parameter Expansion of the Fermion Propagator in an External Field |
|
|
174 | (5) |
|
12.3 Hopping Parameter Expansion of the Effective Action |
|
|
179 | (4) |
|
12.4 The HPE and the Pauli Exclusion Principle |
|
|
183 | (9) |
| 13. WEAK COUPLING EXPANSION (I). THE Φ³-THEORY |
|
192 | (17) |
|
|
|
192 | (3) |
|
13.2 Weak Coupling Expansion of Correlation Functions in the φ³-Theory |
|
|
195 | (6) |
|
13.3 The Power Counting Theorem of Reisz |
|
|
201 | (8) |
| 14. WEAK COUPLING EXPANSION (II). LATTICE QED |
|
209 | (33) |
|
14.1 The Gauge Fixed Lattice Action |
|
|
209 | (7) |
|
14.2 Lattice Feynman Rules |
|
|
216 | (6) |
|
14.3 Renormalization of the Axial Vector Current in One-Loop Order |
|
|
222 | (12) |
|
|
|
234 | (8) |
| 15. WEAK COUPLING EXPANSION (III). LATTICE QCD |
|
242 | (42) |
|
15.1 The Link Integration Measure |
|
|
243 | (4) |
|
15.2 Gauge Fixing and the Faddeev-Popov Determinant |
|
|
247 | (5) |
|
15.3 The Gauge Field Action |
|
|
252 | (5) |
|
15.4 Propagators and Vertices |
|
|
257 | (15) |
|
15.5 Relation Between Λ and the Λ-Parameter of Continuum QCD |
|
|
272 | (3) |
|
15.6 Universality of the Axial Anomaly in Lattice QCD |
|
|
275 | (9) |
| 16. MONTE CARLO METHODS |
|
284 | (33) |
|
|
|
284 | (2) |
|
16.2 Construction Principles for Algorithms. Markov chains |
|
|
286 | (5) |
|
16.3 The Metropolis Method |
|
|
291 | (2) |
|
16.4 The Langevin Algorithm |
|
|
293 | (2) |
|
16.5 The Molecular Dynamics Method |
|
|
295 | (6) |
|
16.6 The Hybrid Algorithm |
|
|
301 | (3) |
|
16.7 The Hybrid Monte Carlo Algorithm |
|
|
304 | (3) |
|
16.8 The Pseudofermion Method |
|
|
307 | (6) |
|
16.9 Application of the Hybrid Monte Carlo Algorithm to Systems with Fermions |
|
|
313 | (4) |
| 17. SOME RESULTS OF MONTE CARLO CALCULATIONS |
|
317 | (66) |
|
17.1 The String Tension and the qq-Potential in the SU(3) Gauge Theory |
|
|
317 | (7) |
|
17.2 The qq-Potential in Full QCD |
|
|
324 | (2) |
|
17.3 Chiral Symmetry Breaking |
|
|
326 | (4) |
|
|
|
330 | (6) |
|
17.5 Hadron Mass Spectrum |
|
|
336 | (9) |
|
|
|
345 | (14) |
|
17.7 Flux Tubes in the qq and qqq-Systems |
|
|
359 | (4) |
|
17.8 The Dual Superconductor Picture of Confinement |
|
|
363 | (10) |
|
17.9 Center Vortices and Confinement |
|
|
373 | (10) |
| 18. PATH-INTEGRAL REPRESENTATION OF THE THERMODYNAMICAL PARTITION FUNCTION FOR SOME SOLVABLE BOSONIC AND FERMIONIC SYSTEMS |
|
383 | (41) |
|
|
|
383 | (1) |
|
18.2 Path-Integral Representation of the Partition Function in Quantum Mechanics |
|
|
384 | (2) |
|
18.3 Sum Rule for the Mean Energy |
|
|
386 | (3) |
|
18.4 Test of the Energy Sum Rule. The Harmonic Oscillator |
|
|
389 | (5) |
|
18.5 The Free Relativistic Boson Gas in the Path Integral Appoach |
|
|
394 | (4) |
|
18.6 The Photon Gas in the Path Integral Approach |
|
|
398 | (3) |
|
18.7 Functional Methods for Fermions. Basics |
|
|
401 | (4) |
|
18.8 Path Integral Representation of the Partition Function for a Fermionic System valid for Arbitrary Time-Step |
|
|
405 | (5) |
|
18.9 A Modified Fermion Action Leading to Fermion Doubling |
|
|
410 | (3) |
|
18.10 The Free Dirac Gas. Continuum Approach |
|
|
413 | (4) |
|
18.11 Dirac Gas of Wilson Fermions on the Lattice |
|
|
417 | (7) |
| 19. FINITE TEMPERATURE PERTURBATION THEORY OFF AND ON THE LATTICE |
|
424 | (61) |
|
19.1 Feynman Rules For Thermal Green Functions in the λφ4-Theory |
|
|
424 | (9) |
|
19.2 Generation of a Dynamical Mass at T not = to 0 |
|
|
433 | (1) |
|
19.3 Perturbative Expansion of the Thermodynamical Potential |
|
|
434 | (6) |
|
19.4 Feynman Rules for QED and QCD at non-vanishing Temperature and Chemical Potential in the Continuum |
|
|
440 | (5) |
|
19.5 Temporal Structure of the Fermion Propagator at T not = to 0 and μ not = to 0 in the Continuum |
|
|
445 | (3) |
|
19.6 The Electric Screening Mass in Continuum QED in One-Loop Order |
|
|
448 | (4) |
|
19.7 The Electric Screening Mass in Continuum QCD in One-Loop Order |
|
|
452 | (3) |
|
19.8 Lattice Feynman Rules for QED and QCD at T not = to 0 and μ not = to 0 |
|
|
455 | (5) |
|
19.9 Particle-Antiparticle Spectrum of the Fermion Propagator at T not = to 0. Naive vs. Wilson Fermions |
|
|
460 | (4) |
|
19.10 The Electric Screening Mass for Wilson Fermions in Lattice QED to One-Loop Order |
|
|
464 | (8) |
|
19.11 The Electric Screening Mass for Wilson Fermions in Lattice QCD to One-Loop Order |
|
|
472 | (10) |
|
19.12 The Infrared Problem |
|
|
482 | (3) |
| 20. NON-PERTURBATIVE QCD AT FINITE TEMPERATURE |
|
485 | (57) |
|
20.1 Thermodynamics on the Lattice |
|
|
485 | (5) |
|
20.2 The Wilson Line or Polyakov Loop |
|
|
490 | (5) |
|
20.3 Spontaneous Breakdown of the Center Symmetry and the Deconfinement Phase Transition |
|
|
495 | (1) |
|
20.4 How to Determine the Transition Temperature |
|
|
496 | (2) |
|
20.5 A Two-Dimensional Model. Test of Theoretical Concepts |
|
|
498 | (14) |
|
20.6 Monte Carlo Study of the Deconfinement Phase Transition in the Pure SU(3) Gauge Theory |
|
|
512 | (8) |
|
20.7 The Chiral Phase Transition |
|
|
520 | (4) |
|
20.8 Some Monte Carlo Results on the High Temperature Phase of QCD |
|
|
524 | (8) |
|
20.9 Some Possible Signatures for Plasma Formation |
|
|
532 | (10) |
| Appendix A |
|
542 | (10) |
| Appendix B |
|
552 | (2) |
| Appendix C |
|
554 | (3) |
| Appendix D |
|
557 | (3) |
| Appendix E |
|
560 | (2) |
| Appendix F |
|
562 | (2) |
| Appendix G |
|
564 | (7) |
| References |
|
571 | (14) |
| Index |
|
585 | |
Shopping Cart
