Gaussian free field and conformal field theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
2013
|
| Schriftenreihe: | Astérisque
353 |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. [131] - 134 |
| Beschreibung: | VII, 136 S. graph. Darst. |
| ISBN: | 9782856293690 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV041371016 | ||
| 003 | DE-604 | ||
| 005 | 20210922 | ||
| 007 | t | ||
| 008 | 131021s2013 d||| |||| 00||| eng d | ||
| 020 | |a 9782856293690 |9 978-2-85629-369-0 | ||
| 035 | |a (OCoLC)859576189 | ||
| 035 | |a (DE-599)GBV769177611 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-824 |a DE-19 |a DE-83 |a DE-29T |a DE-355 |a DE-188 | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60J67 |2 msc | ||
| 084 | |a 81T40 |2 msc | ||
| 100 | 1 | |a Kang, Nam-Gyu |e Verfasser |0 (DE-588)1043865152 |4 aut | |
| 245 | 1 | 0 | |a Gaussian free field and conformal field theory |c Nam-Gyu Kang ; Nikolai G. Makarov |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2013 | |
| 300 | |a VII, 136 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Astérisque |v 353 | |
| 500 | |a Literaturverz. S. [131] - 134 | ||
| 700 | 1 | |a Makarov, Nikolai G. |e Verfasser |0 (DE-588)1043865616 |4 aut | |
| 830 | 0 | |a Astérisque |v 353 |w (DE-604)BV002579439 |9 353 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026819170 | ||
Datensatz im Suchindex
| _version_ | 1804151461347590144 |
|---|---|
| adam_text | CONTENTS
Introduction
.................................................................. 1
Lecture
1.
Fock space fields
................................................. 3
1.1.
Gaussian free field
....................................................... 3
1.2.
Fock space of Gaussian free field and Wick s multiplication
............. 5
1.3.
Fock space correlation functionals
....................................... 7
1.4.
Fock space fields
........................................................ 10
Appendix
2.
Fock space fields as (very) generalized random functions
13
2.1.
Approximation of correlation functionals by elements of the Fock space
. 13
2.2.
Distributional fields
..................................................... 14
2.3.
Insertion operators
...................................................... 18
Lecture
3.
Operator product expansion
................................... 21
3.1.
Definition and first examples
............................................ 21
3.2.
OPE coefficients
......................................................... 23
3.3.
OPE powers and exponentials of Gaussian free field
..................... 24
3.4.
The field
Τ
=
-i J
*
J
.................................................. 26
Lecture
4.
Conformai
geometry of Fock space fields
..................... 29
4.1.
Non-random
conformai
fields
............................................ 29
4.2.
Conformai Fock
space fields
............................................. 31
4.3.
Conformai invariance ....................................................
33
4.4.
Lie derivatives
........................................................... 34
4.5.
Properties of Lie derivatives
............................................. 36
Lecture
5.
Stress tensor and Ward s identities
........................... 39
5.1.
Residue operators
....................................................... 39
5.2.
Stress tensor
............................................................ 40
5.3.
Wards OPEs
............................................................ 41
5.4.
Stress tensor of Gaussian free field
...................................... 43
CONTENTS
5.5.
Ward s identities
........................................................ 44
5.6.
Meromorphic vector fields
............................................... 46
5.7.
Ward s equations in the half-plane
...................................... 48
Appendix
6.
Ward s identities for finite Boltzmaxm-Gibbs ensembles
51
Lecture
7.
Virasoro field and representation theory
..................... 55
7.1.
Virasoro field
............................................................ 56
7.2.
Commutation of residue operators
....................................... 57
7.3.
Virasoro algebra
......................................................... 60
7.4.
Virasoro generators
...................................................... 61
7.5.
Singular vectors
......................................................... 62
Appendix
8.
Existence of the Virasoro field
.............................. 65
Appendix
9.
Operator algebra formalism
................................. 69
9.1.
Construction of (local) operator algebras from holomorphic Fock space
fields
................................................................... 69
9.2.
Radial ordering
.......................................................... 7]
9.3.
Commutation identity and normal ordering
............................. 73
Lecture
10.
Modifications of the Gaussian free field
..................... 77
10.1.
Construction
........................................................... 77
10.2.
Vertex fields
............................................................ 79
10.3.
Level two degeneracy and BPZ equations
.............................. 80
10.4.
Boundary conditions and insertions
.................................... 82
Appendix
11.
Current primary fields and KZ equations
................ 85
11.1.
Current primary fields
................................................. 85
11.2.
KZ equations
............................................................ 87
Lecture
12.
Multivalued
conformai Fock
space fields
.................... 89
12.1.
Chiral
bosome
fields
.................................................... 89
12.2.
Chiral bi-vertex fields
.................................................. 93
12.3.
Rooted vertex fields
.................................................... 96
Appendix
13.
CFT and SLE numerology
................................. 99
Lecture
14.
Connection to SLE theory
....................................103
14.1.
Chorda! SLE
...........................................................103
14.2.
Boundary condition changing operators
................................106
14.3.
Cardy s equations
......................................................108
14.4.
SLE
martingale-observables
............................................
Ill
14.5.
Examples
..............................................................112
Lecture
15.
Vertex
observables
.................................................117
15.1.
Holomorphic 1-point vertex fields
...................................... 117
15-2-
Normalized tensor products
..............................................120
ASTÉRISQUE
353
CONTENTS
vii
15.3.
l-point
martingale-observables
.........................................123
15.4.
Multi-point
observables
................................................125
Bibliography-
..................................................................131
Index
..........................................................................135
SOCIÉTÉ MATHÉMATIQUE DE FRANCE
2013
In these mostly expository lectures, we give an elementary intro¬
duction to
conformai
field theory in the context of probability the¬
ory and complex analysis. We consider statistical
fiele,
and define
Ward functions in terms of their Lie derivatives. Based on this
approach, we explain some equations of
conformai
field theory and
outline their relation to SLE theory.
|
| any_adam_object | 1 |
| author | Kang, Nam-Gyu Makarov, Nikolai G. |
| author_GND | (DE-588)1043865152 (DE-588)1043865616 |
| author_facet | Kang, Nam-Gyu Makarov, Nikolai G. |
| author_role | aut aut |
| author_sort | Kang, Nam-Gyu |
| author_variant | n g k ngk n g m ng ngm |
| building | Verbundindex |
| bvnumber | BV041371016 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)859576189 (DE-599)GBV769177611 |
| discipline | Mathematik |
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| id | DE-604.BV041371016 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:55:11Z |
| institution | BVB |
| isbn | 9782856293690 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026819170 |
| oclc_num | 859576189 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-824 DE-19 DE-BY-UBM DE-83 DE-29T DE-355 DE-BY-UBR DE-188 |
| physical | VII, 136 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spelling | Kang, Nam-Gyu Verfasser (DE-588)1043865152 aut Gaussian free field and conformal field theory Nam-Gyu Kang ; Nikolai G. Makarov Paris Soc. Math. de France 2013 VII, 136 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Astérisque 353 Literaturverz. S. [131] - 134 Makarov, Nikolai G. Verfasser (DE-588)1043865616 aut Astérisque 353 (DE-604)BV002579439 353 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kang, Nam-Gyu Makarov, Nikolai G. Gaussian free field and conformal field theory Astérisque |
| title | Gaussian free field and conformal field theory |
| title_auth | Gaussian free field and conformal field theory |
| title_exact_search | Gaussian free field and conformal field theory |
| title_full | Gaussian free field and conformal field theory Nam-Gyu Kang ; Nikolai G. Makarov |
| title_fullStr | Gaussian free field and conformal field theory Nam-Gyu Kang ; Nikolai G. Makarov |
| title_full_unstemmed | Gaussian free field and conformal field theory Nam-Gyu Kang ; Nikolai G. Makarov |
| title_short | Gaussian free field and conformal field theory |
| title_sort | gaussian free field and conformal field theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026819170&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
| work_keys_str_mv | AT kangnamgyu gaussianfreefieldandconformalfieldtheory AT makarovnikolaig gaussianfreefieldandconformalfieldtheory |