Non-perturbative field theory: from two-dimensional conformal field theory to QCD in four dimensions
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2014
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge monographs on mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVII, 436 S. graph. Darst. |
| ISBN: | 1107424712 9781107424715 9780521662659 |
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| 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 |
| 246 | 1 | 3 | |a Non perturbative field theory |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2014 | |
| 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 | |
| 650 | 0 | 7 | |a Relativistische Quantenfeldtheorie |0 (DE-588)4177686-0 |2 gnd |9 rswk-swf |
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|---|---|
| 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
11
1.9
Path integral quantization
12
1.10
Affine
current algebra
13
1.11
Virasoro algebra
14
2
Conformai
field theory
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
Majorana
fermions
-
an example of a CFT
34
2.13
The Ising model
-
the
m
— 3
unitary minimal model
37
x
(
о
ni
ι
nts
Л
Theories invariant under
aliine
current algebras
39
4.1 Simple finite-dimensional Lie algebras ;19
4.2
Aliine
current algebra
44
4.4
Curren!
ОІМ і.ч
and the Siigawara const
1
net ion
49
.4.]
Primary fields r>l
4.Г.
ALA characters -r>2
;{.(;
Correlators, null
veci
ors
and the Kiii/hnik /aniolodchikov
e(|iiat ion
■>
,4.7
1 Vee ferinion reali/atiuii
·>:)
5.
S
1 Vee Dirac I eniiions and the
/ (
Λ
)
-í
Λ
Wess /iniiino
Witten
model ami cose! models
61
1.1
l-Vom
Tree inassless scalar theory to
lhe W/W
model
(»1
1.2
Реї
Ί
m
bat
ive
conformai invariance °
1.4
ALA. Siii^awaia const nut ion
and
tlu·
Vii asoi
< >
alj .ebra
и
1.1 (
orrelat
ion
lunet
ions
ol
primai y
fields
■ Ι.Γ»
W/W models with boundaries I) bi
alies ^
|.(i C/II coset models 7:]
1.7 (!/(!(<
»set ni<»dels f)
Γ)
Solitons and two-dimensional
integrable
models J
Γ).1
Int
((»duct ion
Г). 2 і
Vo m t
he t lieorv of a massive free
scalai
field to
79
integrable
models
Г).4
(
lassical solitons
86
Γ).Ί
Breathers or doublets
CO
•г)..г)
Quant
uni
solitons
•r).(¡
Inte^rability and facloii/ed S-iuatrix
Гі.7
Van«; Baxter cijiiat ions
95
Г).,Ѕ
The
депегііі
solution of the
S-matľix
Г)Л)
Krom
conformai
field theories to
iul
er
rable
models
101
5.10
Conserved charges and classic,
il int
еці
ability
5.11
Mult ¡local conserved charges
5.12
Quantum
integrable
charges in tlieOf.V) model
5.1.4
Non-local charges and (|Uantuni groups
5.1-1
Intť grahle
spin chain models and
lhe
algebraic
.
Bcthe
ansat
z r
5.15
The
cont
inuuni
t
hennodviiamic Bet he
ansat
/
131
(î
Bosonization „n
(i.l
Λ
lxdiaii boson
i/a t
ion .»a
ii.2 Duality between the Thimng inmlel and the sine-Cordon
mod« 1
^
fi.4
Witten
s non-abelian
bosonization
f».
4
Chiral bosons
Contents xi
6.5 Bosonization
of systems of operators of high
conformai
dimension
159
7
The large ./V limit of two-dimensional models
165
7.1
Introduction
165
7.2
The Gross-Neveu model
166
7.3
The
CP* 1
model 111
PART II TWO-DIMENSIONAL NON-PERTURBATIVE
GAUGE DYNAMICS
8
Gauge theories in two dimensions
—
basics
177
8.1
Pure Maxwell theory
177
8.2
QED-2 Sehwinger s model
178
8.3
Yang Mills theory
179
8.4
Quantum chromodynamics
180
9
Bosonized gauge theories
183
9.1
QED-2 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
YM<¿
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 QCD2 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 hauling energies
250
13.8 Mosern-
haryoii scattering
252
14
Confinement versus screening
265
14.1
Tin4 string tension of
t
he massive
Schwinger
model
265
14.2
The
Schwinger
model in hosonie form
268
14..4
Beyond tin* small mass abelian string tension
268
14.4
Correction to the lending long distance abelian potential
269
14.
Γ)
Finite temperature
271
14.( )
Two-dimensional QCD
272
14.7
Symmetric and antisymmetric representations
276
15
QCD,, eoset models and
BRST
quantization
279
ΙΓι.1
Introduction
279
15.2
The act ion
279
15.3
Two-dimensional Yang Mills theory
282
15.4 Schwinger
model revisited
283
ΙΓ,.Γ)
Back to the YM theory
285
15.
(і
An
alternativo
formulation
287
15.7
The resolution of the puzzle
288
15.8
On bosonized QCD-2 289
15.9
Summary and discussion
290
16
Generalized Yang-Mills theory on a Rioinaiin surface
291
292
291
1(3.1
Introduction
16.2
The partition function of the
ΥΜ·>
theory
16.3
The partition function of yYM2 theories
16.4
Loop averages in the generalized
casi1
16.5
Stringy YM-i theory
16.6
Toward the stringy generalized
YM-¿
16.7
Examples
,
16.8
Summary
PART III FROM TWO TO FOUR DIMENSIONS
17
Conformai invariance
in four-dimensional field theories
and in QCD oiq
17.1
Conformai
symmetry algebra in four dimensions
17.2
Conformai invariance
of fields, Noether currents and ^
conservation laws
17.3
Collinear
and transverse
conformai
transformations
^,
of fields
17.4
Collinear
primary fields and descendants
17.5
Conformai
operator product expansion
Contents xiii
17.6
Conformai
Ward
identities
319
17.7
Conformai invariance and QCD
χ
322
18
Integrability in four-dimensional gauge dynamics
329
18.1
Integrability
of
large
N
fou
r-
dimensional
Λ/
= 4
SYM
330
18.2
High energy scattering and integrability
333
19
Large JV methods in QCD4
337
19.1
Large 7V QCD in four dimensions
337
19.2
Meson phenomenology
343
19.3 Baryons in
the large TV expansion
346
19.4
Scattering processes
352
20
From 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 TV,-
= 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
U
a (I) anomaly
403
23
Summary, conclusions and outlook
407
23.1
General
407
23.2
Conformai invariance
408
23.3
Integrability
410
23.4
Bosonization
411
23.5
Topologica!
field configurations
412
23.6
Confinement versus screening
414
xiv
( oìiteiits
2ІІ.
7
Hadľonir
phenomenology ol two dimensions versus lour
dimensions
2ϋ.Ν
Outlook
420
¡ìcfcìvtu-cs
423
Index A;];]
NON-PERTURBATIVE FIELD THEORY
From Two-Dimensional
Conformai
Field Theory
to QCD in Four Dimensions
Providing a new perspective on quantum field theory, this book gives a ped¬
agogical and up-to-date exposition of non-perturbative methods in relativistic
quantum field theory and introduces the reader to modern research work in
theoretical physics.
It describes in detail non-perturbative methods in quantum field theory,
and explores two-dimensional and four-dimensional gauge dynamics using those
methods. The book concludes with a summary emphasizing the interplay
between two- and four-dimensional gauge theories.
Aimed at graduate students and researchers, this book covers topics from two-
dimensional
conformai
symmetry,
affine Lie
algebras, solitons,
integrable
models,
bosonization and
t Hooft
model, to four-dimensional
conformai invariance, inte-
grability, large
N
expansion, Skyrme model,
monopoles
and
instantons.
Applica¬
tions, first to simple field theories and gauge dynamics in two dimensions, and
then to gauge theories in four dimensions and quantum chromodynamics (QCD)
in particular, are thoroughly described.
Yitzhak
Fris h m
an is a Professor Emeritus at the Weizmann Institute,
Israel, where he has served as Head of the Einstein Centre for Theoretical Physics
and Head of the Department of Particle Physics.
Jacob
SONNENSCHEIN
is a Professor of Physics at Tel Aviv University,
Israel, where he was Head of the Particle Physics Department from
2003
to
2007.
|
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| id | DE-604.BV042058071 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:11:37Z |
| institution | BVB |
| isbn | 1107424712 9781107424715 9780521662659 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027499006 |
| oclc_num | 900861259 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVII, 436 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge monographs on mathematical physics |
| 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 Non perturbative field theory 1. paperback ed. Cambridge Cambridge Univ. Press 2014 XVII, 436 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics 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 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499006&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499006&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Frishman, Yitzhak 1938- Sonnenschein, Jacob Non-perturbative field theory from two-dimensional conformal field theory to QCD in four dimensions 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_alt | Non perturbative field theory |
| 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 | Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd |
| topic_facet | Relativistische Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499006&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=027499006&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT frishmanyitzhak nonperturbativefieldtheoryfromtwodimensionalconformalfieldtheorytoqcdinfourdimensions AT sonnenscheinjacob nonperturbativefieldtheoryfromtwodimensionalconformalfieldtheorytoqcdinfourdimensions AT frishmanyitzhak nonperturbativefieldtheory AT sonnenscheinjacob nonperturbativefieldtheory |