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Index




E6 215, 329 Balmer“Rydberg formula 285, 286, 289,
299, 339
Z2 252“254, 257
Berezin integral 144
γ matrices 180, 293, 302
Bianchi identity 162“164
θ-vacuum 199, 205
Biaxial nematic phase 37
™t Hooft symbol 58
Big desert 336
™t Hooft“Polyakov monopole 43, 55, 73,
Bogomol™nyi bound 18, 49, 50, 57
88, 264
Bogomol™nyi completion 259, 269
1+1 dimensions 238
Bogomol™nyi“Prasad“Sommer¬eld
construction 237, 238, 242
Abelian gauge theory 174
Bogomolnyi inequality 202, 207, 235
Abelian Higgs model 9, 10, 12“14, 19, Bose“Fermi cancelation 245
22, 29, 44, 45, 67, 68, 86
Boson determinant 177
Abrikosov-Vortices 9 BPS equations 243, 244, 258, 259, 261
Action principle 101, 102, 105 BPS-saturated 238, 242, 254
Adjoint representations 343 BRS transformations 215
A¬ne representations 292, 344 BRST charge 131“135, 146, 147, 152
Aharonov“Bohm ¬‚ux 81, 83“86 BRST cohomology 133, 135, 138, 139,
Alexandro¬ compacti¬cation 27 145, 146, 152, 156, 158, 159
Algebras 344 BRST harmonic states 139
Anharmonic oscillators 277 BRST invariance 142, 146, 154, 155, 157
Anomalies 158, 169, 180, 184, 191, BRST operator 127, 136“145, 156“158
194, 198, 199, 210, 215, 216, 218, 220, BRST operator cohomology 142
233“235, 243, 248, 250“253, 260, 266, BRST-Hodge decomposition theorem
267 141
Anomalies, Yang“Mills 338 BRST-laplacian 141
Anomaly, global 253 BRST-multiplets 141
Anomaly, Jacobian 220 BRST-singlets 141
Anomaly, lattice 220
Anomaly, non-abelian 212 C conjugation 275, 293, 306, 309, 310
Anticommuting variables 127 Cabibbo“Kobayashi“Maskawa matrix
Antiparticles 293, 303, 306, 330 298, 331
Automorphism 309, 314, 315, 317“319, Caloron 89
322“327, 332, 333, 350 Canonical formalism 11, 42, 65, 109
Axial current 169, 170, 184“188, Canonical operator formalism 113
190“192, 194“198, 211“213 Casimir e¬ect 65, 84, 85
Axial gauge 53, 76“79, 86, 87, 89“91, 93 Center 31, 69, 73, 87
Axion 210 Center of a group 341
352 Index

Center re¬‚ection 70, 74, 78 Cooper pair 13, 16
Coordinates, collective 226, 245, 247,
Center symmetric ensemble 89
249
Center symmetry 47, 61, 64, 69, 79
Coordinates, harmonic 301
Center vortex 71
Coset 31, 44
Center-symmetric phase 74, 79, 81, 83
Coset space 31, 48, 51, 92
Central charge 111“113, 136, 238, 241,
Cosmological constant 313, 320
243, 250“252, 259, 260, 271, 272
Cosmological term 281
Central extension 241, 259, 260, 322
Coulomb gauge 53, 62, 67
Central unitaries 324“327
Coulomb phase 14
Chamseddine“Connes action 312“314,
Counter terms 152
319
Covariant derivative 10, 38, 58, 125
Charge fractionalization 254
CP(1) 263, 264, 266, 267, 270, 274, 275,
Charge irrationalization 264
277
Charge, topological 170, 200, 201, 203,
CP(N-1) 201
205“207, 209, 238, 241, 242, 259
Critical coupling 18
Charged component 46
Critical points 239, 243“245
Chern character 162“164
Critical temperature 75
Chern“Simons action 63
Crossed helicity 63
Chiral charge 176, 194
Current conservation 185, 188“190, 194,
Chiral fermions 159
197, 213
Chiral super¬eld 256, 257
Curvature scalar 288, 302, 321
Chiral symmetry 173“177, 183“185,
Curvature tensor 177, 198
188, 191, 194, 195, 211, 212, 217, 218,
Cyclic groups 341
221, 228, 235
Chiral transformations 169, 174, 177, Debye screening 68, 75, 86
185, 191, 198, 211, 213, 217, 220 Defect 34, 72, 92
Chirality 219, 223, 224, 227, 293, 303, Degree 28
306, 309, 310, 316, 330 Derivative, covariant 175, 177, 178, 202,
Christo¬el symbols 302 294, 295, 321
Classical BRST transformations 130 Diagonalization gauge 91
Cli¬ord algebra 128 Di¬eomorphism group 309, 314, 342
Co-BRST operator 139, 140, 145 Dirac action 293, 294, 296, 300, 305, 319
Coherence length 17, 18 Dirac equation 295, 304, 311
Commutator algebra 116 Dirac matrices 128
Compactness of a group 341 Dirac monopole 8, 54, 88
Complexi¬cation 342 Dirac operator, eigenvalues 218
Con¬nement 18, 46, 61, 62, 64, 69“71, Dirac string 88, 91
73“75, 79, 81, 83, 89, 205 Direct product 344
con¬nement“decon¬nement transition Director 27, 35
76 Disclination 34
Con¬ning phase 64, 74 Displacement vector 67
Conformal coupling 320 Divergences, UV 167, 177, 180, 184
Conformal invariance 204 Domain wall 34, 237, 238, 254, 258,
Conservation laws 107, 108, 114, 115, 260“262
117 Domain wall fermions 169, 170, 184,
Constants of motion 107, 110, 113 222, 225, 227, 228, 235, 236
Contractible loop 35 Domain walls, supersymmetric 260
Contractible space 20 Dual ¬eld strength 10
Index 353

Duality transformation 18 Gauge invariance 175, 185“188, 190,
191, 193, 194, 196, 204, 212, 214, 292,
Dyons 270
294“296, 299“301
Gauge orbit 34, 51, 52, 54, 57, 70, 71
E¬ective action 81
Gauge string 41, 68, 75
E¬ective potential 68
Gauge symmetries 167, 172
Einbein 101, 105, 115, 118, 119, 150
Gauge theories, chiral 158
Einstein“Hilbert action 288, 301, 314,
Gauge theories, non-abelian 178, 181,
340
201, 206, 211
Endomorphisms 343
Gauge transformation 11“13, 40, 55, 72,
Energy density 43, 47
76, 88
Energy-momentum tensor 124, 241,
Gauge transformations of electro-
251, 252, 266, 288
dynamics 103
Equations, descent 162, 163
Gauge, covariant 174, 177, 178
Equivalence class 15, 22, 44, 51, 57, 58
Gauge, Lorentz 302, 310
Equivalence relation 25
Gauge, symmetric 310, 311
Euclidean geometry 285
Gauge, temporal 148, 204, 205, 210
Euclidean space 170
Gauss“Stokes theorem 129
Euclidean time 170“172, 205

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