Foundations of quantum chromodynamics: an introduction to perturbative methods in gauge theories
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2010
|
| Edition: | 3. ed. |
| Series: | World scientific lecture notes in physics
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 409 S. Ill., graph. Darst. |
| ISBN: | 9789812793546 9812793542 9789812793539 9812793534 |
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| 245 | 1 | 0 | |a Foundations of quantum chromodynamics |b an introduction to perturbative methods in gauge theories |c T Muta |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2010 | |
| 300 | |a XVI, 409 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a World scientific lecture notes in physics |v 78 | |
| 650 | 4 | |a Champs de jauge (Physique) | |
| 650 | 4 | |a Chromodynamique quantique | |
| 650 | 4 | |a Perturbation (Mathématiques) | |
| 650 | 4 | |a Gauge fields (Physics) | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 4 | |a Quantum chromodynamics | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface to the Third Edition
vii
Preface to the Second Edition
ix
Preface to the First Edition
xi
Chapter
1.
Introduction
1.1.
General Survey
1
1.2.
Quarks and Color
7
1.2.1.
Low-lying baryon states
9
1.2.2.
Quark confinement
10
1.2.3.
Indirect experimental evidences
11
1.3.
Need for Asymptotic Freedom
15
1.4.
Notation and Conventions
21
Chapter
2.
Elements of Quantum Chromodynamics
2.1.
Gauge Principle
24
2.1.1.
Electrodynamics
24
2.1.2.
Yang-Mills theories
29
2.2.
Quantization
35
2.2.1.
Trouble with the canonical quantization
35
2.2.2.
Quantization in the Feynman
39
functional-integral formalism
2.2.3.
Quantization of gauge fields
47
2.2.4.
Fermions
53
2.3.
Feynman Rules
57
2.3.1.
S
matrix and Green functions
57
2.3.2.
φ3
theory
71
2.3.3.
Quantum chromodynamics
81
2.3.4.
Simple example in e+e~ annihilation
95
2.3.5.
Covariant canonical quantization of
98
gauge fields
2.4.
Regularization
103
2.4.1.
Review of regularization schemes
103
2.4.2.
Dimensional regularization
109
2.4.3.
Preliminary remarks on renormalization
119
schemes
xiv CONTENTS
2.5.
Renormalization 124
2.5.1.
Power counting
124
2.5.2.
Renormalizable interactions
128
2.5.3.
Renormalization in
φ3
theory
132
2.5.4.
BPHZ method in
φ3
theory
149
2.5.5.
Quantum chromodynamics
157
2.5.6.
Generalized Ward-Takahashi identities
173
Chapter
3.
Renormalization Group Method
3.1.
Renormalization Group
180
3.1.1.
Finite renormalization
180
3.1.2.
Group of finite renormalizations
183
3.2.
Renormalization group equations
186
3.2.1.
Renormalization group equation in the
186
MS scheme
3.2.2.
The renormalization group equation in other
192
schemes
3.3.
Solution of the Renormalization Group Equations
199
3.3.1.
Solution of the
t Hooft-
Weinberg
equation
199
3.3.2.
Behavior of the solution
201
3.4.
Asymptotic Freedom
206
3.4.1.
Renormalization group functions in QCD
206
3.4.2.
Asymptotic freedom in QCD
214
3.4.3.
Renormalization group functions in other
216
theories
3.5.
Anomalous Dimensions
217
Chapter
4.
Operator Product Expansion
4.1.
Operator Products
222
4.1.1.
Composite operators
222
4.1.2.
Product of currents in deep inelastic
225
scatterings
4.1.3.
Product of currents in e+e~ annihilations
231
4.2.
Operator-product Expansion in Perturbation
234
Theory
4.2.1.
Free field theory
234
4.2.2.
The
parton
model
238
4.2.3.
Renormalization of composite operators
243
4.2.4.
Proof of the operator product expansion
249
4.2.5.
Light-cone expansion
262
4.3.
Coefficient Functions
263
4.3.1.
Singularity in coefficient functions
263
4.3.2.
Renormalization group equations
264
CONTENTS
Chapter
5.
Physical Applications
5.1.
Total Cross Section for
e+e
Annihilations
268
5.1.1.
Renormalization group equation
268
5.1.2.
Order-g2 correction
270
5.1.3.
Higher-order corrections
277
5.2.
Deep Inelastic Lepton-hadron Scatterings
278
5.2.1.
Moment sum rules for structure functions
278
5.2.2.
Renormalization-group-improved
283
perturbation
5.2.3.
Flavor structure of composite operators
289
5.2.4.
The nonsinglet part
291
5.2.5.
The singlet part
297
5.2.6.
Experimental tests
300
5.3.
Renormalization-scheme Dependence
307
5.3.1.
Renormalization-scheme dependence of
307
perturbative predictions
5.3.2.
β
function and anomalous dimensions
311
5.3.3.
e+e- annihilations and deep inelastic
312
scatterings
5.4.
Jets
315
5.4.1.
qq jets in
e+e
annihilations
315
5.4.2.
Higher order effects
320
5.4.3.
Experimental observation
321
5.5.
Factorization and the Drell-Yan Process
322
Chapter
6.
Infrared Divergences
6.1.
One-loop Example
331
6.1.1.
Origin of infrared divergences
331
6.1.2.
Regularization
334
6.1.3.
Cancellation of infrared divergences
338
6.2.
Proof of the Soft-photon Cancellation in QED
345
6.2.1.
Soft-photon emission
345
6.2.2.
Virtual photons
351
6.2.3.
Cancellation
354
6.3.
General Arguments for Infrared Cancellations
355
6.3.1.
Infrared divergence in QCD
355
6.3.2.
The Kinoshita-Poggio-Quinn theorem
358
6.3.3.
The Kinoshita-Lee-Nauenberg theorem
364
Appendix A
:
One-loop Contribution to Superficially
371
Divergent Feynman Amplitudes in QCD
Appendix
В
:
Useful Formulas involving the SU(N)
380
Generators
AppendixC
: Renormalization
Constante
in QCD 382
Appendix
D
:
Feynman Rules
384
Bibliography
384
Index 403
|
| adam_txt |
CONTENTS
Preface to the Third Edition
vii
Preface to the Second Edition
ix
Preface to the First Edition
xi
Chapter
1.
Introduction
1.1.
General Survey
1
1.2.
Quarks and Color
7
1.2.1.
Low-lying baryon states
9
1.2.2.
Quark confinement
10
1.2.3.
Indirect experimental evidences
11
1.3.
Need for Asymptotic Freedom
15
1.4.
Notation and Conventions
21
Chapter
2.
Elements of Quantum Chromodynamics
2.1.
Gauge Principle
24
2.1.1.
Electrodynamics
24
2.1.2.
Yang-Mills theories
29
2.2.
Quantization
35
2.2.1.
Trouble with the canonical quantization
35
2.2.2.
Quantization in the Feynman
39
functional-integral formalism
2.2.3.
Quantization of gauge fields
47
2.2.4.
Fermions
53
2.3.
Feynman Rules
57
2.3.1.
S
matrix and Green functions
57
2.3.2.
φ3
theory
71
2.3.3.
Quantum chromodynamics
81
2.3.4.
Simple example in e+e~ annihilation
95
2.3.5.
Covariant canonical quantization of
98
gauge fields
2.4.
Regularization
103
2.4.1.
Review of regularization schemes
103
2.4.2.
Dimensional regularization
109
2.4.3.
Preliminary remarks on renormalization
119
schemes
xiv CONTENTS
2.5.
Renormalization 124
2.5.1.
Power counting
124
2.5.2.
Renormalizable interactions
128
2.5.3.
Renormalization in
φ3
theory
132
2.5.4.
BPHZ method in
φ3
theory
149
2.5.5.
Quantum chromodynamics
157
2.5.6.
Generalized Ward-Takahashi identities
173
Chapter
3.
Renormalization Group Method
3.1.
Renormalization Group
180
3.1.1.
Finite renormalization
180
3.1.2.
Group of finite renormalizations
183
3.2.
Renormalization group equations
186
3.2.1.
Renormalization group equation in the
186
MS scheme
3.2.2.
The renormalization group equation in other
192
schemes
3.3.
Solution of the Renormalization Group Equations
199
3.3.1.
Solution of the
't Hooft-
Weinberg
equation
199
3.3.2.
Behavior of the solution
201
3.4.
Asymptotic Freedom
206
3.4.1.
Renormalization group functions in QCD
206
3.4.2.
Asymptotic freedom in QCD
214
3.4.3.
Renormalization group functions in other
216
theories
3.5.
Anomalous Dimensions
217
Chapter
4.
Operator Product Expansion
4.1.
Operator Products
222
4.1.1.
Composite operators
222
4.1.2.
Product of currents in deep inelastic
225
scatterings
4.1.3.
Product of currents in e+e~ annihilations
231
4.2.
Operator-product Expansion in Perturbation
234
Theory
4.2.1.
Free field theory
234
4.2.2.
The
parton
model
238
4.2.3.
Renormalization of composite operators
243
4.2.4.
Proof of the operator product expansion
249
4.2.5.
Light-cone expansion
262
4.3.
Coefficient Functions
263
4.3.1.
Singularity in coefficient functions
263
4.3.2.
Renormalization group equations
264
CONTENTS
Chapter
5.
Physical Applications
5.1.
Total Cross Section for
e+e'
Annihilations
268
5.1.1.
Renormalization group equation
268
5.1.2.
Order-g2 correction
270
5.1.3.
Higher-order corrections
277
5.2.
Deep Inelastic Lepton-hadron Scatterings
278
5.2.1.
Moment sum rules for structure functions
278
5.2.2.
Renormalization-group-improved
283
perturbation
5.2.3.
Flavor structure of composite operators
289
5.2.4.
The nonsinglet part
291
5.2.5.
The singlet part
297
5.2.6.
Experimental tests
300
5.3.
Renormalization-scheme Dependence
307
5.3.1.
Renormalization-scheme dependence of
307
perturbative predictions
5.3.2.
β
function and anomalous dimensions
311
5.3.3.
e+e- annihilations and deep inelastic
312
scatterings
5.4.
Jets
315
5.4.1.
qq jets in
e+e'
annihilations
315
5.4.2.
Higher order effects
320
5.4.3.
Experimental observation
321
5.5.
Factorization and the Drell-Yan Process
322
Chapter
6.
Infrared Divergences
6.1.
One-loop Example
331
6.1.1.
Origin of infrared divergences
331
6.1.2.
Regularization
334
6.1.3.
Cancellation of infrared divergences
338
6.2.
Proof of the Soft-photon Cancellation in QED
345
6.2.1.
Soft-photon emission
345
6.2.2.
Virtual photons
351
6.2.3.
Cancellation
354
6.3.
General Arguments for Infrared Cancellations
355
6.3.1.
Infrared divergence in QCD
355
6.3.2.
The Kinoshita-Poggio-Quinn theorem
358
6.3.3.
The Kinoshita-Lee-Nauenberg theorem
364
Appendix A
:
One-loop Contribution to Superficially
371
Divergent Feynman Amplitudes in QCD
Appendix
В
:
Useful Formulas involving the SU(N)
380
Generators
AppendixC
: Renormalization
Constante
in QCD 382
Appendix
D
:
Feynman Rules
384
Bibliography
384
Index 403 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Muta, Taizo 1937- |
| author_GND | (DE-588)172269105 |
| author_facet | Muta, Taizo 1937- |
| author_role | aut |
| author_sort | Muta, Taizo 1937- |
| author_variant | t m tm |
| building | Verbundindex |
| bvnumber | BV023223176 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.3.Q35 |
| callnumber-search | QC793.3.Q35 |
| callnumber-sort | QC 3793.3 Q35 |
| callnumber-subject | QC - Physics |
| classification_rvk | UO 5700 UO 5730 |
| classification_tum | PHY 413f |
| ctrlnum | (OCoLC)498396991 (DE-599)BVBBV023223176 |
| dewey-full | 531.16 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.16 |
| dewey-search | 531.16 |
| dewey-sort | 3531.16 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 3. ed. |
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| id | DE-604.BV023223176 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:16:53Z |
| indexdate | 2024-07-09T21:13:28Z |
| institution | BVB |
| isbn | 9789812793546 9812793542 9789812793539 9812793534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016409034 |
| oclc_num | 498396991 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | XVI, 409 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| series | World scientific lecture notes in physics |
| series2 | World scientific lecture notes in physics |
| spelling | Muta, Taizo 1937- Verfasser (DE-588)172269105 aut Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories T Muta 3. ed. Singapore [u.a.] World Scientific 2010 XVI, 409 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier World scientific lecture notes in physics 78 Champs de jauge (Physique) Chromodynamique quantique Perturbation (Mathématiques) Gauge fields (Physics) Perturbation (Mathematics) Quantum chromodynamics Eichtheorie (DE-588)4122125-4 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Quantenchromodynamik (DE-588)4128082-9 gnd rswk-swf Quantenchromodynamik (DE-588)4128082-9 s Störungstheorie (DE-588)4128420-3 s DE-604 Eichtheorie (DE-588)4122125-4 s World scientific lecture notes in physics 78 (DE-604)BV000819327 78 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409034&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Muta, Taizo 1937- Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories World scientific lecture notes in physics Champs de jauge (Physique) Chromodynamique quantique Perturbation (Mathématiques) Gauge fields (Physics) Perturbation (Mathematics) Quantum chromodynamics Eichtheorie (DE-588)4122125-4 gnd Störungstheorie (DE-588)4128420-3 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| subject_GND | (DE-588)4122125-4 (DE-588)4128420-3 (DE-588)4128082-9 |
| title | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories |
| title_auth | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories |
| title_exact_search | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories |
| title_exact_search_txtP | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories |
| title_full | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories T Muta |
| title_fullStr | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories T Muta |
| title_full_unstemmed | Foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories T Muta |
| title_short | Foundations of quantum chromodynamics |
| title_sort | foundations of quantum chromodynamics an introduction to perturbative methods in gauge theories |
| title_sub | an introduction to perturbative methods in gauge theories |
| topic | Champs de jauge (Physique) Chromodynamique quantique Perturbation (Mathématiques) Gauge fields (Physics) Perturbation (Mathematics) Quantum chromodynamics Eichtheorie (DE-588)4122125-4 gnd Störungstheorie (DE-588)4128420-3 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| topic_facet | Champs de jauge (Physique) Chromodynamique quantique Perturbation (Mathématiques) Gauge fields (Physics) Perturbation (Mathematics) Quantum chromodynamics Eichtheorie Störungstheorie Quantenchromodynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409034&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000819327 |
| work_keys_str_mv | AT mutataizo foundationsofquantumchromodynamicsanintroductiontoperturbativemethodsingaugetheories |