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Rivasseau V. — From Perturbative to Constructive Renormalization
Rivasseau V. — From Perturbative to Constructive Renormalization

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Название: From Perturbative to Constructive Renormalization

Автор: 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: en

Рубрика: Физика/Квантовая теория поля/Ренормализационная группа/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 336

Добавлена в каталог: 27.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\phi^{4}_{4}$ theory      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 $\phi^{4}_{4}$      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 $\phi^{4}_{4}$ theory      123
Planar $\phi^{4}_{4}$ theory, planar $\phi^{4}_{4}$ theory graphs, planar $\phi^{4}_{4}$ theory Feynman rules      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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