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Benfatto G., Gallavotti G. — Renormalization Group
Benfatto G., Gallavotti G. — Renormalization Group



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Название: Renormalization Group

Авторы: Benfatto G., Gallavotti G.

Аннотация:

Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems.

The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.


Язык: en

Рубрика: Физика/Квантовая теория поля/Ренормализационная группа/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 143

Добавлена в каталог: 27.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Annihilation operator      12 14
Anomalous dimension      56 64 71 74 120
Anomalous effective potential      59 68 111 120
Anomalous fixed point      74
Anomalous flow      73
Anomalous potential      63
Anomalous scaling      18 62 66 71
Anomalous transformation      62
asymptotic freedom      34 36 37 51 54 86 87
Auxiliary field      24
Bare constant      17 50
Bare coupling      34
Bare mass      8
beta function      38 50 52 65 66 69 70 73 74 87 92 94 126 127 133
Beta functional      50 51 60 65 66 68 71
Bogoliubov approximation      77
Bogoliubov model      75 78 79 90
Bose condensate      15 16
Bose condensation      3 12 19 37 75 80 81 87
Bose gas      12 14 16 17 22 124 126
Boundary condition      5 8 13 28 118
chemical potential      13 16 17 42 77
Computer-assisted proof      74
Correlation function      10
Covariance      7
Creation operator      12 14
Critical exponents      97
Critical indices      5 64
Critical point      10 3 5 22 35 40 53 56 64 97 98
Critical temperature      5 64
Cutoff      8 10 76 86 106 127
Dimensional potential      44
Dimensionless field      34 82
Dimensionless potential      27 32 34 35 38 42 44 61 63 72
Effective potential      19 25 26 27 32 34 35 36 41 47 52 56 62 64 66 71 79 81 111 116
Effective potential singularity      52
Eigenfunction      31
Endpoint      114
Epsilon expansion      70
Euclidean field      3 106
Euclidean field theory      8
Fermi gas      16
Fermi liquid      3 12 20 22 25 28 29 30 32 37 40 41 42 49 51 52 54 64 68 70
Fermi momentum      16 17 43
Fermi sphere      12 105
Fermi surface      3 13 22 24 54 56 68
Fermi velocity      24
Feynman graph      50 61 90 92 111 114 116 119 126
Field dimension      26 31
Fixed point      62 67 69
Free energy      9
Functional integral      12 13 19 22 25 75
Gauge symmetry      42 43
Gaussian measure      8 10 15 19 75 76 78 124
Gaussian process      7
Generating functional      9 63 111 120
grand canonical ensemble      13
Grassmann algebra      13 19 25
Grassmannian integral      108 109
Grassmannian integration      13 19 21 66 106
Grassmannian variable      106 109
Gross — Neveu model      51
Ground state      13
Hadamard inequality      108 110
Hamiltonian      5 12
Heat equation      39
Hermite polynomials      29 30
Hierarchical model      26 74
Infrared problem      9 10 23 25 26 28 29 34 35 36 37 40 41 49 52 53 55 56
Irrelevant operator      31 42 43 49 82 84
Irrelevant part      39 42 43 112
KAM      38
Kernel      27 61 116 118
Landau — Ginsburg model      6
Linear flow      35
Linearized flow      34
Local operator      31
Localization operator      39 40 57 82 84 112 117 126
Luttinger model      68 69
Marginal operator      37 60 84 85
Mass      18 42
mean field      35 53
Multiscale decomposition      8 22 24 25 32
N! bound      50 92
Nonlocal relevant operator      32
Nonrenormalized expansion      47
Nontrivial fixed point      62 64 74
Normal critical behavior      71
Normal scaling      74
Occupation number      13
Old renormalization theory      29
Operator      31
Pairing      30 31 108
Partition function      6 7 81
Perturbation expansion      32
Perturbation theory      17 38 42 52 55 62 72
Physical constant      17
Physical coupling      52
Physical mass      18 23
Probability measure      11
Propagator      7 13 19 24 30 56 59 68 75 81 85 92 104 109 124 126
Propagator matrix      79 85 124 127
QFT      29 47 54 97
Quasi particle      25 28 41 43 100
Recursion relation      26 27
Relevant operator      31 32 36 38 42 60 70 82 83 84 115
Relevant part      42 112
Relevant term      31
Renormalizable theory      50
Renormalization constant      84 87 89
Renormalization group      3 19 29 36 38 40 55 56 65 74
Renormalization group flow      26 29 53 69 87
Renormalization transformation      66
Running coupling      36 37 40 42 47 49 50 52 60 62 65 69 70 72 80 81 84 87 89 123
Running coupling singularity      52
Running effective potentials      22 26
SCALE      27 34 38
Scale invariance      3
Scaling beta function      65
Scaling dimension      26
Schwinger function      9 13 14 16 17 18 35 56 62 63 66 71 72 76 77 80 81 104 111 120 123
Short memory      67
Sound speed      79 86 87
Superfluid behavior      75 76 79 80 82
Thermodynamic function      5
TREE      32 46 48 52 111 114 121 127
Tree distance      32
Tree formalism      52
Tree vertex      114
Trivial critical behavior      71
Trivial fixed point      29 72
Trivial vertex      114
Triviality      36 51
Triviality conjecture      54 98
Trotter's product formula      14
Truncated Schwinger function      9 20 43 120
Ultraviolet problem      10 22 23 25 26 28 29 34 36 37 40 44 49 52
Volume dependence      27
Wave function correction      53
Wick monomial      29 30 31 32 40
Wick order      30 43
Wick rule      14 30 108
Wilson recursion relation      26 96 97
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