Non-perturbative field theory: from two-dimensional conformal field theory to QCD in four dimensions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Enth. Literaturverz. S. [423] - 431 und Index |
| Beschreibung: | XVII, 436 S. graph. Darst. |
| ISBN: | 9780521662659 |
Internformat
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| 100 | 1 | |a Frishman, Yitzhak |d 1938- |e Verfasser |0 (DE-588)142577928 |4 aut | |
| 245 | 1 | 0 | |a Non-perturbative field theory |b from two-dimensional conformal field theory to QCD in four dimensions |c Yitzhak Frishman ; Jacob Sonnenschein |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2010 | |
| 300 | |a XVII, 436 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 500 | |a Enth. Literaturverz. S. [423] - 431 und Index | ||
| 650 | 0 | |a Field theory (Physics) | |
| 650 | 0 | |a Perturbation (Quantum dynamics) | |
| 650 | 0 | 7 | |a Relativistische Quantenfeldtheorie |0 (DE-588)4177686-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Sonnenschein, Jacob |e Verfasser |0 (DE-588)142578037 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804143051122147328 |
|---|---|
| adam_text | Contents
Preface
page
xv
Acknowledgements
xviii
PART I NON-PERTURBATIVE METHODS IN
TWO-DIMENSIONAL FIELD THEORY
1
From massless free scalar field to
conformai
field
theories
3
1.1
Complex geometry
3
1.2
Free massless scalar field
4
1.3
Symmetries of the classical action
5
1.4
Mode expansion
6
1.5
Noether currents and charges
7
1.6
Canonical quantization
7
1.7
Radial quantization
9
1.8
Operator product expansion
H
1.9
Path integral quantization
12
1.10
Affine
current algebra
13
1.11
Virasoro algebra
14
2
Conformai
field theory
17
2.1
Conformai
symmetry in two dimensions
17
2.2
Primary fields
18
2.3
Conformai
properties of the energy-momentum tensor
20
2.4
Virasoro algebra for CFT
21
2.5
Descendant operators
22
2.6
Hubert space of states
23
2.7
Unitary CFT and
Кас
determinant
25
2.8
Characters
28
2.9
Correlators and the
conformai
Ward identity
29
2.10
Crossing symmetry, duality and bootstrap
31
2.11
Verlinde s formula
33
2.12
Free
Majorána
fermions
-
an example of a CFT
34
2.13
The Ising model
-
the
m
= 3
unitary minimal model
37
χ
Contents
3
Theories invariant under
affine
current algebras
39
3.1
Simple finite-dimensional Lie algebras
39
3.2 Affine
current algebra
44
3.3
Current OPEs and the Sugawara construction
49
3.4
Primary fields
51
3.5
ALA characters
52
3.6
Correlators, null vectors and the Knizhnik-Zamolodchikov
equation
53
3.7
Pree fermion
realization
55
3.8
Pree
Dirac
fermions
and the U(N)
58
4
Wess-Zumino-
Witten
model and coset models
61
4.1
From free massless scalar theory to the WZW model
61
4.2
Perturbative
conformai invariance
65
4.3
ALA, Sugawara construction and the Virasoro algebra
66
4.4
Correlation functions of primary fields
67
4.5
WZW models with boundaries
-
D branes
71
4.6
G/H coset models
73
4.7
G/G coset models
75
5 Solitons
and two-dimensional
integrable
models
79
5.1
Introduction
79
5.2
From the theory of a massive free scalar field to
integrable
models
79
5.3
Classical solitons
81
5.4
Breathers or doublets
86
5.5
Quantum solitons
88
5.6
Integrability and factorized S-matrix
92
5.7
Yang-Baxter equations
94
5.8
The general solution of the S-matrix
95
5.9
From
conformai
field theories to
integrable
models
99
5.10
Conserved charges and classical integrability
101
5.11
Multilocal conserved charges
104
5.12
Quantum
integrable
charges in the O(N) model
107
5.13
Non-local charges and quantum groups
108
5.14
Integrable
spin chain models and the algebraic
Bethe ansatz HI
5.15
The continuum thermodynamic Bethe ansatz
125
6
Bosonization
131
6.1
Abelian bosonization
132
6.2
Duality between the Thirring model and the sine-Gordon model
136
6.3
Witten s non-abelian bosonization
139
6.4
Chiral bosons
148
Contents
xi
6.5
Bosonization of systems of operators of high
conformai
dimension
159
7
The large
N
limit of two-dimensional models
165
7.1
Introduction
165
7.2
The Gross-Neveu model
166
7.3
The CPN~l model
171
PART II TWO-DIMENSIONAL NON-PERTURBATIVE
GAUGE DYNAMICS
8
Gauge theories in two dimensions
—
basics
177
8.1
Pure Maxwell theory
177
8.2
QED2
-
Schwinger s model
178
8.3
Yang-Mills theory
179
8.4
Quantum chromodynamics
180
9
Bosonized gauge theories
183
9.1
QED2
-
The massive
Schwinger
model
183
9.2
Abelian bosonization of flavored QCD2
185
9.3
Non-abelian bosonization of QCD2
187
10
The
t Hooft
solution of 2d QCD
191
10.1
Scattering of mesons
198
10.2
Higher 1/N corrections
201
11
Mesonic spectrum from current algebra
203
11.1
Introduction
203
11.2
Universality of
conformai
field theories coupled to YM2
203
11.3
Mesonic spectra of two-current states
206
11.4
The adjoint vacuum and its one-current state
216
12
DLCQ and the spectra of QCD with fundamental and
adjoint
fermions
223
12.1
Discretized light-cone quantization
223
12.2
Application of DLCQ to QCD2 with fundamental
fermions
224
12.3
The spectrum of QGD2 with adjoint
fermions
228
13
The baryonic spectrum of multiflavor QCD2 in the strong
coupling limit
237
13.1
The strong coupling limit
237
13.2
Classical soliton solutions
239
13.3
Semi-classical quantization and the baryons
240
13.4
The baryonic spectrum
247
13.5
Quark flavor content of the baryons
247
13.6
Multibaryons
249
xii
Contents
13.7
States, wave functions and binding energies
250
13.8
Meson-baryon scattering
252
14
Confinement versus screening
265
14.1
The string tension of the massive
Schwinger
model
265
14.2
The
Schwinger
model in bosonic form
268
14.3
Beyond the small mass abelian string tension
268
14.4
Correction to the leading long distance abelian potential
269
14.5
Finite temperature
271
14.6
Two-dimensional QCD
272
14.7
Symmetric and antisymmetric representations
276
15
QCD2, coset models and
BRST
quantization
279
15.1
Introduction
279
15.2
The action
279
15.3
Two-dimensional Yang-Mills theory
282
15.4
Schwinger
model revisited
283
15.5
Back to the YM theory
285
15.6
An alternative formulation
287
15.7
The resolution of the puzzle
288
15.8
On bosonized QCDi
289
15.9
Summary and discussion
290
16
Generalized Yang—Mills theory on a Riemann surface
291
16.1
Introduction
291
16.2
The partition function of the
FM 2
theory
292
16.3
The partition function of
g YM2
theories
296
16.4
Loop averages in the generalized case
297
16.5
Stringy YMi theory
299
16.6
Toward the stringy generalized
Y M
2
301
16.7
Examples
302
16.8
Summary
304
PART III FROM TWO TO POUR DIMENSIONS
17
Conformai invariance
in four-dimensional field theories
and in QCD
309
17.1
Conformai
symmetry algebra in four dimensions
310
17.2
Conformai invariance
of fields, Noether currents and
conservation laws
312
17.3
Collinear
and transverse
conformai
transformations
of fields
314
17.4
Collinear
primary fields and descendants
316
17.5
Conformai
operator product expansion
318
Contents xiii
17.6
Conformai
Ward
identities
319
17.7
Conformai invariance and QCDa
322
18
Integrabiłity
in four-dimensional gauge dynamics
329
18.1
Integrabiłity
of large
N
four-dimensional
Λί
= 4
SYM
330
18.2
High energy scattering and
integrabiłity
333
19
Large
N
methods in QCD4
337
19.1
Large
N
QCD in four dimensions
337
19.2
Meson phenomenology
343
19.3 Baryons
in the large
N
expansion
346
19.4
Scattering processes
352
20
Prom 2d bosonized baryons to 4d Skyrmions
355
20.1
Introduction
355
20.2
The Skyrme action
355
20.3
The baryon as a Skyrmion
361
20.4
The Skyrme model for Nf
=3 367
21
From two-dimensional solitons to four-dimensional
magnetic
monopoles
371
21.1
Introduction
371
21.2
The Yang-Mills Higgs theory
-
basics
372
21.3
Topological solitons and magnetic
monopoles
373
21.4
The t Hooft-Polyakov magnetic
monopole
solution
376
21.5
Charge quantization
377
21.6
Zero modes, time-dependent solutions and dyons
378
21.7
BPS monopoles
and dyons
381
21.8
Montonen Olive duality
382
21.9 Nahm
construction of multimonopole solutions
383
21.10
Moduli space of
monopoles
386
22
Instantons
of QCD
389
22.1
The basic properties of the
instanton
389
22.2
The ADHM construction of
instantons
394
22.3
On the moduli space of
instantons
396
22.4
Instantons and tunneling between the vacua of the YM theory
400
22.5
Instantons, theta
vacua and the Ua(1) anomaly
403
23
Summary, conclusions and outlook
407
23.1
General
407
23.2
Conformai invariance
408
23.3
Integrabiłity 410
23.4
Bosonization
411
23.5
Topological field configurations
412
23.6
Confinement versus screening
414
xiv Contents
23.7 Hadronic
phenomenology of two dimensions versus four
dimensions
416
23.8
Outlook
420
References
423
Index
433
|
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| author_GND | (DE-588)142577928 (DE-588)142578037 |
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| id | DE-604.BV036489795 |
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| institution | BVB |
| isbn | 9780521662659 |
| language | English |
| lccn | 2009036354 |
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| spelling | Frishman, Yitzhak 1938- Verfasser (DE-588)142577928 aut Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions Yitzhak Frishman ; Jacob Sonnenschein 1. publ. Cambridge [u.a.] Cambridge University Press 2010 XVII, 436 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Enth. Literaturverz. S. [423] - 431 und Index Field theory (Physics) Perturbation (Quantum dynamics) Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd rswk-swf Relativistische Quantenfeldtheorie (DE-588)4177686-0 s DE-604 Sonnenschein, Jacob Verfasser (DE-588)142578037 aut http://assets.cambridge.org/97805216/62659/cover/9780521662659.jpg Cover image DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9780521662659.pdf Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020412418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frishman, Yitzhak 1938- Sonnenschein, Jacob Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions Field theory (Physics) Perturbation (Quantum dynamics) Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd |
| subject_GND | (DE-588)4177686-0 |
| title | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions |
| title_auth | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions |
| title_exact_search | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions |
| title_full | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions Yitzhak Frishman ; Jacob Sonnenschein |
| title_fullStr | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions Yitzhak Frishman ; Jacob Sonnenschein |
| title_full_unstemmed | Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions Yitzhak Frishman ; Jacob Sonnenschein |
| title_short | Non-perturbative field theory |
| title_sort | non perturbative field theory from two dimensional conformal field theory to qcd in four dimensions |
| title_sub | from two-dimensional conformal field theory to QCD in four dimensions |
| topic | Field theory (Physics) Perturbation (Quantum dynamics) Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd |
| topic_facet | Field theory (Physics) Perturbation (Quantum dynamics) Relativistische Quantenfeldtheorie |
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