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Gambini R., Pullin J. — Loops, Knots, Gauge Theories and Quantum Gravity
Gambini R., Pullin J. — Loops, Knots, Gauge Theories and Quantum Gravity

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Название: Loops, Knots, Gauge Theories and Quantum Gravity

Авторы: Gambini R., Pullin J.

Аннотация:

This text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a review of calculus in loop space and the fundamentals of loop representations. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theory, the braid algebra and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research. This self-contained introduction will be of interest to graduate students and researchers in theoretical physics and applied mathematics.


Язык: en

Рубрика: Физика/Квантовая теория поля/Квантовая гравитация/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 321

Добавлена в каталог: 02.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
2+1 gravity      230
Abelian group of loops      (see group of loops Abelian)
Acceleration terms      203 204
ADM      164
Aether      240
Alexander      245 262
Algebraic constraint      31 37 262 286
Ambient isotopy      240
Annihilation operator      94 99
Anomaly      298
Area, derivative      2
Area, operator      225
Arf invariant      262
Ashtekar variables      (see New variables)
Bargmann quantization, harmonic oscillator      103
Bargmann quantization, Maxwell theory      105
Bianchi identities      13
biology      248
Borromean rings      239
Bracket polynomial      247
Braid group      243
Braid group, intersecting braids      251
Braid group, representations      249
Brillouin zone      158
Casson      262
Cauchy, completion      78
Cauchy, surface      165
Characteristic function      197
Chen integral      5
Chern — Simons      185 254 292
Cluster approximation      150
Coherent states      95
confinement      124
Connection derivative      (see Derivative connection)
Connection representation      179
Constraint algebra      177
Conway      245 262
Covariant lattice theory      133
Creation operator      94 99
Cylindrical measure      79
Deficit angle      232
Degeneracy problem      185
Derivative, connection      17
Derivative, contact      21
Derivative, loop      8
DeSitter      186
Diffeomorphism      22 46 47 79 169
Differential constraint      31
Dirac, quantization      61
Dirac, theory      54
Disorder parameter      126
Einstein equations      164
Einstein — Maxwell theory      215
Extended loop representation, Maxwell      109
Extended loop representation, quantum gravity      275
Extended loop representation, quantum gravity, constraints      280
Extended loop representation, quantum gravity, physical states      289
Extended loop representation, quantum gravity, regularization      291
Extended loop representation, quantum gravity, wavefunctions      277
Extended loops, generators      36
Extended loops, group of      32
Extended loops, holonomy      68
Extended loops, loop coordinates      38
Extended loops, special extended group      33
Extrinsic curvature      166
Factor ordering      180
Fermion doubling      158
Fierz identity      257
Fock representation      92
Gauge theories, lattice SU(2)      144
Gauge theories, lattice Z(2)      133
Gauge theories, Maxwell      88
Gauge theories, Yang — Mills      58 113
Gauge transformations      26 60
Gauge transformations, large      58
Gauss, law      60 91 216
Gauss, linking number      49 128 239 248 272
General relativity, Lagrangian formulation      164
Group of loops      2
Group of loops, Abelian      89
Group of loops, infinitesimal generators      7
Group of loops, representations      25
Hamiltonian constraint      169 176 179
Hamiltonian constraint, action on Wilson loop      182
Hamiltonian constraint, extended representation      282
Hamiltonian constraint, loop representation      190 195 197
Hamiltonian lattice gauge theory      138
Hamiltonian, Yang — Mills theory      59 119
Higgs      126
Hilbert space      57
Holomorphic      103
Holonomy      1 6
Homfly polynomial      247
Homotopy group      233
Hoops      6
Inequalities      86
Intersecting loops      117 183
Isotopy      240
Jones polynomial      246 254 263 265
Kalb — Ramond fields      218
Kauffman bracket      247 264
Knot      47
Knot, class      196
Knot, intersecting      251
Knot, polynomials      242
Knot, theory      239
Lattice      131
Loop representation      72
Loop representation, Maxwell theory      96
Loop representation, quantum gravity      188
Loop representation, quantum gravity constraints      189 192
Loop representation, SU(2) Yang — Mills theory      118
Loop representation, SU(N) Yang — Mills theory      121
Loop representation, wavefunctions      84
Loop, average in QCD      (see Makeenko — Migdal equation)
Loop, definition      2
Loop, transform      74 76
Makeenko — Migdal equation      115
Mandelstam, covariant derivative      13
Mandelstam, identities      63
Markov moves      244
Maxwell theory      (see gauge Theories Maxwell)
Measures on non linear spaces      77
Metropolis      132
Moduli space      233
Multiloops      85 123
Multitangents      30
New variables      171 175
Non-canonical algebra      80
Normal ordering      94
Palatini action      173
Path ordered      4
Paths      7
plaquette      134
Propagator, Chern — Simons theory      261
Propagator, Maxwell symmetric      100
Quaxk      125
Reality conditions      178
Reconstruction property      67
Regular isotopy      240
Regularization      196
Reidemeister moves      240
Ricci identity      15
Schwarz space      77
Self-dual action      174
Sigma models      114
Skein relations      245
Spinors      210
Staggered Fermion      159
Stokes theorem, non — Abelian      16
Surface representation      220
T algebra      80
Tetradic general relativity      172
Thin loop      5
Topological field theories      253
Transfer matrix      136
Transverse Dirac delta      91
TREE      5
t’Hooft operator      126
Unification      215
Weaves      221
Weyl fermions      209
Wheeler — DeWitt equation      171
Wilson loops      63
Winding number      127
Writhe      247
Yang-Mills theories      (see Gauge theories Yang-Mills)
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