Table of Contents
Preface v
Photos of Yi-Shi Duan vii
1 SU(2) Gauge Theory and Electrodynamics with N Magnetic Monopoles Yi-Shi Duan and Mo-Lin Ge 1
1.1 Introduction 1
1.2 Decomposition of gauge potential and its inner structure 2
1.3 Electrodynamics of magnetic monopoles and electrical particles system in the SU(2) gauge theory 4
1.4 Features of the solution of monopoles' electrodynamical system and topological conservative current 8
1.5 Sourceless solution of SU(2) gauge field and magnetic monopole 11
1.6 U(l) gauge potential of electromagnetic tensor Kμν 12
Bibliography 15
2 Abelian Decomposition of QCD Y. M. Cho 17
2.1 Introduction 18
2.2 Abelian decomposition: a review 20
2.3 Abelian decomposition of SU(3) QCD 22
2.4 Abelian dominance and monopole condensation in QCD 25
2.5 Quark and chromon model and quarkonium-glueball mixing 31
2.6 Monoball: vacuum fluctuation of monopole condensation 34
2.7 Vacuum decomposition 36
2.8 Einstein's theory: gauge theory of Lorentz group 40
2.9 Abelian decomposition of Einstein's theory: restricted gravity 42
2.10 Canonical momentum versus kinematic momentum 44
2.11 Proton spin crisis problem: present status and a new resolution 46
2.12 Closing remarks 52
Bibliography 55
3 How Can We Understand Quark Confinement in Quantum Yang-Mills Theory? Kei-Ichi Kondo 59
3.1 Introduction 59
3.2 Decomposition of the Yang-Mills field and extension to SU(N) gauge group 61
3.3 Non-Abelian Stokes theorem for the Wilson loop operator and gauge-invariant magnetic monopole 63
3.4 Lattice formulations and numerical simulations 63
3.5 Summary 71
Bibliography
4 Asymmetrical Input-output Control in Cavity Quantum Electrodynamics Yifu Zhu 77
4.1 Introduction 77
4.2 Theoretical model and analysis 78
4.3 Numerical results 82
4.4 Conclusion 85
Bibliography
5 Energy and Angular Momentum in Gravity Theories Rong-Gen Cai and Li-Ming Cao 89
5.1 Introduction 90
5.2 Noether currents and conserved quantities 93
5.2.1 Noether currents 94
5.2.2 Theories without background fields 96
5.2.3 Energy-momentum tensor of matter fields 99
5.2.4 Noether currents and energy of matter fields 99
5.2.5 Canonical energy-momentum tensors of matter fields 102
5.2.6 Pseudo tensor and energy-momentum tensor for gravitational field 106
5.2.7 Vielbein, semimetric, four-legs, and tetrad 109
5.2.8 Gravitational energy-momentum can not be locally defined 111
5.2.9 Komar mass and angular momentum 112
5.3 Global definitions 115
5.3.1 General definition on conserved quantities 115
5.3.2 Global quantities at spacelike infinity 117
5.3.3 Global quantities at null infinity 126
5.4 Quasi-local definitions 131
5.4.1 Geometry of codimension-2 surface 132
5.4.2 Misner-Sharp energy 139
5.4.3 Hawking mass 141
5.4.4 Brown-York quasi-local energy-moment urn tensor 145
5.4.5 Other quasi-local definitions 151
5.5 Conclusion and discussion 151
5.6 Asymptotically AdS spacetimes 153
5.7 An example: Kerr-AdS spacetime 159
5.8 Asymptotically dS spacetimes 160
Bibliography 165
6 Gravitational Energy and the Gauge Theory Perspective Chiang-Mei Chen and James M. Nester 169
6.1 Introduction 170
6.2 Some historical background 170
6.2.1 Automatic conservation of the source and gauge fields 170
6.3 Noether's 1918 contribution 171
6.4 Energy-momentum pseudotensors and the Hamiltonian 171
6.5 The Hamiltonian approach 172
6.6 Gauge and geometry 172
6.7 Geometry: kinematics and dynamics 173
6.8 The Poincaré gauge theory of gravity 175
6.8.1 Topological terms 176
6.9 The covariant Hamiltonian formulation 176
6.10 Application to the PG and GR 179
6.10.1 Preferred Hamiltonian boundary terms 180
6.11 The reference choice 180
6.11.1 4D isometric matching 181
6.11.2 An optimal choice 182
6.12 Summary 183
Bibliography 185
7 Energy-Momentum in General Relativity Xiaoning Wu and Xiao Zhang 189
7.1 Energy-momentum of gravitational systems 189
7.1.1 The total conserved quantities for matter fields 189
7.1.2 The total conserved quantities for gravity 192
7.1.3 Duan's energy-momentum 194
7.1.4 ADM total energy and linear momentum 195
7.1.5 Bondi's energy-momentum 196
7.2 Equivalence 197
7.3 Positivity of the total energy 200
7.4 Positive cosmological constant 202
7.5 Acknowledgement 206
Bibliography 207
8 Introduction to Extra Dimensions and Thick Braneworlds Yu-Xiao Liu 211
8.1 Introduction 211
8.2 Some extra dimension theories 213
8.2.1 KK theory 213
8.2.2 Non-compact extra dimension: domain wall model 216
8.2.3 Large extra dimensions: ADD braneworld model 219
8.2.4 Warped extra dimension: RS braneworld models 221
8.3 Solutions of thick brane models in extended theories of gravity 224
8.3.1 Metric f(R) theory 228
8.3.2 Palatini f(R) theory 232
8.3.3 Eddington inspired Born-Infeld theory 235
8.3.4 Scalar-tensor theory 236
8.3.5 f(T) theory 240
8.4 Localization of bulk matter fields 242
8.4.1 Scalar fields 243
8.4.2 Vector fields 245
8.4.3 Kalb-Ramond fields 250
8.4.4 Fermion fields 252
8.5 Summary 257
Bibliography 261
Appendix A Chronicle of Prof. Yi-Shi Duan's life 277
Appendix B Chronicle of Prof. Yi-Shi Duan's life 315
Appendix C List of Prof. Yi-Shi Duan's Publications 341
