Non-perturbative renormalization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ u.a.
World Scientific
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 290 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9812792392 9789812792396 |
Internformat
MARC
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| 020 | |a 9789812792396 |9 978-981-279239-6 | ||
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| 100 | 1 | |a Mastropietro, Vieri |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Non-perturbative renormalization |c Vieri Mastropietro |
| 264 | 1 | |a Hackensack, NJ u.a. |b World Scientific |c 2008 | |
| 300 | |a XI, 290 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Renormalization (Physics) | |
| 650 | 4 | |a Quantum field theory | |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Renormierung |0 (DE-588)4128419-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Renormierung |0 (DE-588)4128419-7 |D s |
| 689 | 0 | 1 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111188&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017111188 | ||
Datensatz im Suchindex
| _version_ | 1804138608862429184 |
|---|---|
| adam_text | Contents
Preface
v
Introduction
to Renormalization
1
1.
Basic Notions
3
1.1
Relativistic quantum field theory
.............. 3
1.1.1
Quantum fields
................... 3
1.1.2
Functional integrals
................. 5
1.1.3
Perturbative renormalization
............ 8
1.2
Classical statistical mechanics
................ 12
1.2.1
Phase transitions
.................. 12
1.2.2
Universality and non-universality
......... 14
1.3
Condensed Matter
...................... 16
1.3.1
Electrons in a crystal
................ 16
1.3.2
The free Fermi gas
.................. 19
1.3.3
Fermi liquids
..................... 21
1.3.4
Luttinger liquids and BCS superconductors
.... 23
2.
Fermionic Functional Integrals
27
2.1 Grassmann
variables
..................... 27
2.2
Grassmaim measures
..................... 29
2.3
Truncated expectations
................... 31
2.4
Properties of Grassmaim integrals
............. 32
2.
õ Gallavotti-Xicoló
tree expansion
.............. 33
2.6
Feynman graphs
....................... 39
2.7
Determinant bounds for simple expectations
........ 42
viii NON-PERTURBATIVE RENORMALIZATION
2.8
The Brydges-Battle-Federbush
representation
....... 45
2.9
The Gawedzki-Kupiainen-Lesniewski formula
....... 51
Quantum Field Theory
57
3.
The Ultraviolet Problem
in Massive QED2
59
3.1
Regularization
and cut-offs
................. 59
3.2
Integration of the bosons
.................. 61
3.3
Propagator decomposition
.................. 63
3.4
Renormalized expansion
................... 66
3.5
Feynman graph expansion
.................. 68
3.6
Convergence of the renormalized expansion
........ 69
3.7
Determinant bounds
..................... 72
3.8
The short memory property
................. 75
3.9
Extraction of loop lines
................... 75
3.10
The 2-point
Schwinger
function
............... 79
3.11
The Yukawa model
...................... 79
4.
Infrared Problem and Anomalous Behavior
81
4.1
Anomalous dimension
.................... 81
4.2
Renormalization
....................... 82
4.3
Modification of the fermionic interaction
.......... 83
4.4
Bounds for the renormalized expansion
........... 89
4.5
The beta function at lowest orders
............. 96
4.6
Boundedness of the flow
................... 99
4.7
The 2-point
Schwinger
function
............... 101
5.
Ward Identities and Vanishing of the Beta Function
105
5.1 Schwinger
functions and running couplings
........ 105
5.2
Ward identities in presence of cut-offs
........... 107
5.3
The correction identity
.................... 109
5.4
The Schwinger-Dyson equation
............... 115
5.5
Analysis of the cut-off corrections
.............. 118
5.6
Vanishing of Beta function
.................. 120
5.7
Non-perturbative Adler-Bardeen theorem
......... 122
5.8
Further remarks
....................... 123
6.
Thining and Gross-Neveu Models
125
Contents
ix
6.1
The Thirring model
..................... 125
6.2
Removing the fermionic ultraviolet cut-off before the
bosonic one
.......................... 126
6.3
Removing the bosonic ultraviolet cut-off before the
fermionic one
......................... 128
6.4
The Gross-Neveu model
................... 132
7.
Axioms Verification and Wilson
Fermions
133
7.1
Osterwalder-Schrader axioms
................ 133
7.2
Lattice regularization and fermion doubling
........ 135
7.3
Integration of the doubled
fermions
............. 137
7.4
Lattice
fermions
....................... 138
8.
Infraed QED4 with Large Photon Mass
143
8.1
Regularization
........................ 143
8.2
Tree expansion
........................ 145
Lattice Statistical Mechanics
147
9.
Universality in Generalized Ising Models
149
9.1
The nearest neighbor Ising model
.............. 149
9.2
Heavy and light
Majorana
fermions.............
153
9.3
Generalized Ising models
................... 156
9.4
Fermionic representation of the generalized Ising model
. 157
9.5
Integration of the ^-variables................
159
9.6
Integration of the light
fermions
............... 160
9.7
Correlation functions and the specific heat
......... 164
10.
Nonuniversality in Vertex or
Isotropie Ashkin-
Teller Models
165
10.1
Ashkin-Teller or Vertex models
............... 165
10.2
Fermionic representation
................... 167
10.3
Anomalous behaviour
.................... 170
10.4
Simmetry properties
..................... 171
10.5
Integration of the light
fermions
............... 175
10.6
The specific heat
....................... 177
11.
Universality-Nonuniversality Crossover in the Ashkin-
Teller Model
181
NON-PERTURBATIVE RENORMALIZATION
11.1
The anisotropic AT model
.................. 181
11.2
Anomalous universality
................... 183
11.3
Integration of the
χ
variables
................ 185
11.4
Integration of the
φ
variables: first regime
......... 188
11.5
Integration of the
φ
variables: second regime
....... 192
11.6
Critical behaviour
...................... 195
Quantum Liquids
199
12.
Spinless Luttinger
Liquids
201
12.1
Fermions on a
chain
..................... 201
12.2
Grassman
representation
................... 203
12.3
Luttinger liquid behavior
.................. 204
12.4
The ultraviolet integration
.................. 207
12.5
Quasi-particle fields
..................... 209
12.6
The flow of the running coupling constants
........ 213
12.7
Density correlations
..................... 215
12.8
Quantum spin chains
..................... 219
12.9
Crystals and quasi-crystals
................. 222
13.
The Id Hubbard Model
225
13.1
Spinning
fermions
...................... 225
13.2
Tlie
effective potential
.................... 226
13.3
The flow of the running coupling constants
........ 228
13.4
The auxiliary model
..................... 231
13.5
The effective renormalizations
................ 236
13.6
Attractive interactions
.................... 237
14.
Fermi Liquids in Two Dimensions
239
14.1
Interacting
Fermions
in
rf
= 2................ 239
14.2
Multiscale integration
.................... 242
14.3
Bounds for the Feymnan graphs
.............. 245
14.4
The sector decomposition
.................. 246
14.5
The sector lemma
....................... 250
14.6
Bounds for the tree expansion
................ 253
14.7
Flow of riming coupling constants
............. 257
14.8
Other results in rf
= 2.................... 260
Contents xi
15. BCS Model
with Long Range Interaction
263
15.1
BCS model
.......................... 263
15.2
Partial Hubbard-Stratonovich transformation
....... 266
15.3
Corrections to the mean field
................ 268
Appendix A The Ising Model Fermionic Representation
273
A.I The
Grassmann
representation of the 2d Ising model with
open boundary conditions
.................. 273
A.
2
The
Grassmann
representation of the 2d Ising model with
periodic boundary conditions
................ 283
Bibliography
287
|
| any_adam_object | 1 |
| author | Mastropietro, Vieri |
| author_facet | Mastropietro, Vieri |
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| author_sort | Mastropietro, Vieri |
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| callnumber-first | Q - Science |
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| callnumber-raw | QC174.17.R46 |
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| callnumber-sort | QC 3174.17 R46 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 UO 4020 |
| ctrlnum | (OCoLC)191658548 (DE-599)BVBBV035306397 |
| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3 |
| dewey-search | 530.14/3 |
| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035306397 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:54Z |
| institution | BVB |
| isbn | 9812792392 9789812792396 |
| language | English |
| lccn | 2008298664 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017111188 |
| oclc_num | 191658548 |
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| owner | DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM |
| physical | XI, 290 S. Ill., graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Mastropietro, Vieri Verfasser aut Non-perturbative renormalization Vieri Mastropietro Hackensack, NJ u.a. World Scientific 2008 XI, 290 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Renormalization (Physics) Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Renormierung (DE-588)4128419-7 gnd rswk-swf Renormierung (DE-588)4128419-7 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111188&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mastropietro, Vieri Non-perturbative renormalization Renormalization (Physics) Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Renormierung (DE-588)4128419-7 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4128419-7 |
| title | Non-perturbative renormalization |
| title_auth | Non-perturbative renormalization |
| title_exact_search | Non-perturbative renormalization |
| title_full | Non-perturbative renormalization Vieri Mastropietro |
| title_fullStr | Non-perturbative renormalization Vieri Mastropietro |
| title_full_unstemmed | Non-perturbative renormalization Vieri Mastropietro |
| title_short | Non-perturbative renormalization |
| title_sort | non perturbative renormalization |
| topic | Renormalization (Physics) Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Renormierung (DE-588)4128419-7 gnd |
| topic_facet | Renormalization (Physics) Quantum field theory Quantenfeldtheorie Renormierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111188&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mastropietrovieri nonperturbativerenormalization |