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Rivasseau V. — From Perturbative to Constructive Renormalization
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Название: From Perturbative to Constructive RenormalizationАвтор: Rivasseau V. Аннотация: The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques. Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization.
Язык: Рубрика: Физика /Квантовая теория поля /Ренормализационная группа /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1991Количество страниц: 336Добавлена в каталог: 27.09.2005Операции: Положить на полку |
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200—209 1/N expansion 124—130 282—283 Algebraic cluster expansion 163—164 Almost local subgraphs 66 Amplitude 42—48 Amplitude of a Mayer configuration 186 Amplitude of a polymer 178 ASSIGNMENT 63 asymptotic freedom 8—9 123—124 272 291 294 Auxiliary field 283 Bare expansion 113 Battle — Federbush theorem 180—181 BBF cluster expansion, GJS cluster expansion 195 BBF or Brydges — Battle — Federbush cluster expansion 195 beta function 133 141—142 269—271 Bethe — Salpeter equation 199 Bipeds 83—85 Bogoliubov recursion 82—85 Border vertex functions, inside vertex functions 42 Borel plane 56 Borel plane summability 55 BPH theorem 5 BPHZ scheme 86 Bubble, bubble graph 5 Callan — Symanzik function see "Beta function" Cayley's theorem 49 Classification of forests 94—95 Closed graphs 89 101 Closed graphs forests 101 Closed graphs, gates 216 Closure 101 Cluster expansion 156 171—186 Completely convergent graphs 59 configurations 186 Connected functions 34—35 Constructive renormalization 253—261 Contraction scheme 38 Convergent assignments 74 Convergent assignments, polymers 219 Convergent polymer 219 Coordination number 38 Counterterms 75—85 Cutoffs 27—34 Dangerous forests 92—93 Decay, horizontal 62 Decay, vertical 70 Degree of convergence 41 Diagram 40 Domination 185 221—233 305—308 Effective expansion 111—122 Effective expansion, constants 113 118—119 264—266 Effective expansion, perturbation theory 112 Effective expansion, phase space expansion 252—261 Euclidean field theory 15 20—22 Faddeev — Popov determinant 293 Faddeev — Popov, operator 314—317 Feynman amplitude 42—44 Feynman amplitude, diagram, Feynman amplitude graph 38—40 Feynman amplitude, gauge 292—293 Feynman diagram 40 Feynman gauge 292—293 Feynman — Kac formula 18 20 Forests 86 Free field 16—17 24—26 Garding Wightman axioms 19 Gauge transformations 292 Gauge, non-Abelian Gauge theories 289 Gaussian measure 24—33 Gell-Mann — Low formula 18 Ghosts 293 GJS or Glimm — Jaffe — Spencer cluster expansion 195 graphs 38—42 Gribov problem 309 Gribov problem, copies 309 314—315 Gribov problem, first-region 316—317 Gribov problem, horizon 314 Gribov problem, strong, weak-phenomenon 309—315 Gross — Neveu model 272—288 Hard core interaction 186 Horizontal line, horizontal line direction 64—65 Incidence matrix 38 Index assignment 63 Index assignment, space 63 Infrared 241 Infrared asymptotic freedom 244 instantons 149 Landau gauge 309 Large order behavior 144 Lattice regularization 33—34 Leading-log behavior 6—7 Line, Horizontal line, vertical line 64—65 Lipatov method 146 Lipatov method, upper-bound 153 Local factorial principle 160 Local polymer, renormalized polymer 255 Localization cube 234 Matrix models 125—130 Mayer expansion 186—194 Mayer expansion, configurations 186 Mayer expansion, link 187 Momentum representation 47 Momentum representation, conservation 250—251 Momentum representation, slices 61 Momentum slice decomposition 61—63 Multiscale representation 63 Nelson's bound 202—203 Nevanlinna — Sokal theorem 55 One particle irreducible functions (1PI) 35 Open gates, closed gates 216 Open graphs, gates 216 Open graphs, open graphs quadrupeds 101 Ordered tree 50 Orthogonal polynomials 129 Osterwalder — Schrader axioms 21—22 Overlapping divergences 75 p-particle irreducibility 195—199 Pair of cubes cluster expansion 174 Parametric representation 50—53 Perturbative renormalization 74—110 Phase space 63 Phase space, expansion 210—271 Planar 123 Planar 125—127 Polymer 178 Polymer, bound 180 Polymer, i-polymers 219 Power counting 70 Pressure 172 Production index 230—232 Propagator 24 28 34 61—62 156 293 303 Propagator, domain 157—158 pth order cluster expansion 195—199 Quadrupeds 85 R operator 85 Renormalization group 112—113 Renormalized constants 121—122 Renormalon 6—8 81 Running constants see "Effective constants" S-matrix 17 Safe forests 93—94 Schwinger functions 20 Slavnov — Taylor identities 302—304 Sobolev inequality 147 Strong connection 216 Strongly connected domains 217 Superficial degree of convergence 41 Symanzik polynomials 50—51 Symmetry factor, number 39—40 43—44 Thirring model (massive) 272 TREE 48—50 Triviality 7 268—271 Uniform BPH theorem 88 Uniform Weinberg theorem 65 Useful counterterms, useless counterterms 8 79—80 Useful, useless counterterms 79—80 Usefully renormalized amplitudes 100 110 Vector models 127 272 Vertex functions 35 Vertex, domain 154 Vertical cluster expansion 212—216 Vertical line, decoupling 212—220 Vertical line, direction 64—64 65 Vertical line, expansion 156 Volume effect 183 Ward identities 302—304 Wave function constant 23 Weak coupling, triviality 269 Weinberg theorem 59—60 Wick ordering 200 Wiener measure 26 Wiener measure, paths 156 Yang — Mills action 292 Zimmermann's forests 85—86 Zimmermann's forests, formula 85
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