Conformal quantum field theory in D-dimensions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Mathematics and its applications
376 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 461 S. Ill. |
| ISBN: | 0792341589 |
Staff View
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| 245 | 1 | 0 | |a Conformal quantum field theory in D-dimensions |c by Efim S. Fradkin and Mark Ya. Palchik |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XII, 461 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications |v 376 | |
| 650 | 7 | |a Champs, Théorie quantique des |2 ram | |
| 650 | 7 | |a Conforme invarianten |2 gtt | |
| 650 | 7 | |a Conforme veldentheorie |2 gtt | |
| 650 | 7 | |a Hilbertruimten |2 gtt | |
| 650 | 7 | |a Kwantumveldentheorie |2 gtt | |
| 650 | 4 | |a Conformal invariants | |
| 650 | 4 | |a Quantum field theory | |
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| 689 | 0 | 1 | |a Konforme Feldtheorie |0 (DE-588)4312574-8 |D s |
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| 700 | 1 | |a Palčik, Mark Ja. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface 1
I Goals and Perspectives 3
1. A Problem of the Effective Interaction in an Asymptotic Region
and Gonformal Symmetry 3
2. Quantum Fields in Conformal Theory .. 9
3. Renormalized Schwinger Dyson Equations in the Framework
of Conformal Kinematics 14
4. A Review of Branches and Results in Conformal Theory 23
4.1. Main Directions 27
4.2. The Results 30
5. Conformal Group and its Representations. Introductory Remarks and Nota¬
tions 37
II Global Conformal Symmetry and
Hilbert Space 45
1. The Structure of Conformal Theory in Minkowski Space— a Brief Review.45
2. Conformal Symmetry Conditions 49
2.1. Global Transformations 49
2.2. Infinitesimal Transformations 51
2.3. Conformal Inversion 53
2.4. A General Solution to Conformal .Symmetry Conditions 56
3. Conformal Fields in Two Dimensions 59
3.1. Irreducible Representations of the Conformal Group 59
3.2. Spectrality 62
3.3. Irreducible Representations of Universal Covering Group 63
3.4. Global Transformations of Conformal Fields 67
3.5. Irreducible Fields and Physical Fields 71
3.6. Fields in Compactified and Covering Spaces 74
4. Conformal Fields in £ dimensional Minkowski Space 75
4.1. Basic States y (a:)|0) and Spectrality 75
4.2. Irreducible Representations of Universal Covering
Group of the Conformal Group 78
4.3. Irreducible Fields 81
4.4. Irreducible Fields and Spectrality 83
4.5. Physical Fields 84
4.6. Global Conformal Transformations of Physical Fields 87
4.7. Tensor Fields 89
5. A Structure of Hilbert Space 92
III Euclidean Formulation of the Conformal
Theory 99
1. Classification and Orthogonality of Euclidean Conformal Fields 99
2. Invariant Averages of Euclidean Spinor and Tensor Fields 103
2.1. Tensor Fields 103
2.2. Invariant Functions of Pseudo Tensor Fields 106
2.3. Invariant Functions of Spinor Fields 108
3. An Invariance of Renormalized Equations of the
Schwinger Dyson System. Conformal Partners 109
3.1. A Conformal Invariance of Skeleton Expansions 109
3.2. Amputation Conditions 115
3.3. Tensor Fields 117
4. Electromagnetic and Gravitational Interactions
as a Consequence of Conformal Symmetry 120
5. Operator Expansions of Euclidean Fields
and Conformal Partial Wave Expansions 124
6. Quasilocal Invariant Functions 135
IV Approximate Methods of Calculating
Critical Indices 143
1. Conformal Bootstrap 143
2. Calculation and Summation of Skeleton Graphs. Preliminary Remarks... 146
3. Calculation of Skeleton Graphs in the Simplest Model 148
4. Bootstrap Equations in the A /?4 Theory 151
5. Approximate Methods for Calculating Dimensions in the A^ 4 theory 154
6. Summation of Skeleton Parquet Graphs 161
V Spontaneous Breakdown of Conformal
Symmetry 163
1. Method of Calculation of a Vacuum Field 163
2. Thirring Model 167
VI Ward Identities 171
1. Ward Identities in Conformal Theory 171
1.1. Preliminary Remarks 171
1.2. Local Currents 172
2. Conformal Ward Identities in Two Dimensional Field Theory 175
3. Local Ward Identities and Conformal Symmetry 180
3.1. Local Ward Identities in Relativistic Theory 180
3.2. Conformally Invariant Ward Identities for the Green Functions
of the Current 185
3.3. Conformally Invariant Ward Identities for the Green Functions
of the Energy Momentum Tensor 192
4. Anomalous Ward Identities 196
VII Contribution of Electromagnetic and Gravita¬
tional Interactions into the General Solution of
Ward Identities 205
1. Two Ways to Define the Current and the Energy Momentum Tensor in Con¬
formal Theory 205
2. Irreducible Components of the Current and the Potential 206
3. The Propagator of the Current and the Transversal Sector 214
4. Irreducible Components of the Energy Momentum Tensor
and the Metric Field 217
5. The Propagator of the Metric Field and the Longitudinal Sector 221
6. The Propagator of the Energy Momentum Tensor
and the Transversal Sector 223
7. Decoupling of Electromagnetic and Gravitational Contributions
into the General Solution of Ward Identities 228
8. Conditions Decoupling the Direct (non Gauge) Interaction
of the Matter Fields 230
9. Solution of Ward Identities In Two Dimensional Field Theory 236
VIII Dynamical Sector of the Hilbert Space . 241
1. Definition of Dynamical Sector ,,,..,., , ,.... 241
2. Solution of Ward Identities for the Green Functions of the Current 246
3. Secondary Fields, Generated by Energy Momentum Tensor , ¦ ¦ 254
4. Conformally Invariant Regularization of Lagrangean Equations ,,,.,.,... 260
4.1. Interaction of Scalar Fields in D dimensionsional Space 260
4.2. The Thirring and Pure Gauge Models, as the Simplest Examples 264
4.3. The Solution of the Wess Zumino Witten Model , 268
5. Conformally Invariant Solutions of Lagrangean Equations 273
6. A Model Defined by Two Generations of Secondary Fields in the Space of
Even Dimension D 4.., ,...., ,.,.,. 279
7. A Dynamical Sector of Two Dimensional Conformal Field Theory 287
8. Models in Two Dimensional Space ,...,....,... 294
8.1. Models Defined by Fields Qi and Q3 , 294
8.2. Ising Model 299
8.3. A Model Defined by Two Generations of Secondary Fields ,,.,, ,,,,,, 300
9. Infinite Dimensional Symmetry of Two Dimensional Conformal Theories . 304
IX Conformal Invariance in Gauge Theories . 317
1. Gauge Invariance in a Quantum Conformal Field Theory , 317
2. Combined Conformal Transformations of Gauge Fields , ,. 319
3. Invariance of the Generating Functional of a Gauge Field in a Non Abelian
Case , ,.., 321
4. Global Conformal Transformations of Gauge Fields 326
5. Conformal Ward Identities 329
6. Conformal Bootstrap in Non Abelian Gauge Theories 333
7. An Open Conformal String in Quantum Electrodynamics 336
8. Symmetry Group of a Straight String 338
9. Calculation of Invariant Two and Three Point Green Functions
of a Straight String 341
10. Calculation of Scale Dimension of a String in QED 344
X Special Features of Conformal Transformation of
Current, Energy Momentum Tensor and Gauge
Fields 347
1. Degenerate Conformal Transformations . 347
2. Conformal Transformations of Current and of Electromagnetic Field 349
3. Maxwell Equations as a Consequence of Equivalence of Conformal Group
Representations 356
4. The Skeleton Theory and the Bootstrap Program in QED 358
5. Conformal Transformations in Linear Gravity 363
6. Modified Conformal Transformations of the Energy Momentum Tensor
and of the Metric 366
7. Equations of Linear Gravity as a Consequence of Equivalence of
Representations 369
Appendix I. Casimir Operators and Irreducible Representations of Con¬
formal Group of 4 Dimensional Minkowski Space 373
Appendix II. Fourier Transforms of Euclidean and Minkowski Spaces In*
variant Functions 379
Appendix III. Calculation of Euclidean Quasilocal Invariant Three point
Functions 383
Appendix IV. An Invariance Under Subgroups SO{D 1,2) and SO{D) x
50(2) 386
Appendix V. The Derivation of the Anomalous Ward Identities for Green
Functions {T^T^ipip) and {j^T^ip^) 390
Appendix VI. Explicit Form of Invariant Green Functions (Psipj^). ¦ ¦ ¦ 398
Appendix VII. Partial Wave Expansion of Current Green Functions . 403
1. The Structure of Partial Wave Expansions 403
2. Calculation of the Kernels of Partial Wave Expansions 406
Appendix VIII. Explicit Form of the Invariant Green Function (Ps fiT^) for
s = 2 and the Anomalous Ward Identity 411
Appendix IX. Partial Wave Expansion of the Energy Momentum Tensor
Green functions 414
1. The Structure of Partial Wave Expansion 414
2. Partial Wave Expansion of the Green Function (T^(pxf) 418
3. Solution of Conformal Ward Identities. The Contribution of Fields
Ps to Partial Wave Expansions 424
4. Calculating the Kernels of Partial Wave Expansions of the Green
Functions of the Energy Momentum Tensor 427
5. Derivation of Ps Fields Green Functions 430
Appendix X. Basic Integral Relations 432
Appendix XI. Calculation of Green Functions {Psip... p) and (Ps /?TMi/) in
Two Dimensional Space 437
Appendix XII. Calculation of Integrals in Two Dimensional Space ... 444
Bibliography 451
Index 458
|
| any_adam_object | 1 |
| author | Fradkin, Efim S. 1924-1999 Palčik, Mark Ja |
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| callnumber-subject | QC - Physics |
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| ctrlnum | (OCoLC)34990178 (DE-599)BVBBV011049908 |
| dewey-full | 530.1/43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/43 |
| dewey-search | 530.1/43 |
| dewey-sort | 3530.1 243 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV011049908 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:10Z |
| institution | BVB |
| isbn | 0792341589 |
| language | English Russian |
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| physical | XII, 461 S. Ill. |
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| series2 | Mathematics and its applications |
| spelling | Fradkin, Efim S. 1924-1999 Verfasser (DE-588)118965441 aut Conformal quantum field theory in D-dimensions by Efim S. Fradkin and Mark Ya. Palchik Dordrecht [u.a.] Kluwer 1996 XII, 461 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 376 Champs, Théorie quantique des ram Conforme invarianten gtt Conforme veldentheorie gtt Hilbertruimten gtt Kwantumveldentheorie gtt Conformal invariants Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Konforme Feldtheorie (DE-588)4312574-8 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Konforme Feldtheorie (DE-588)4312574-8 s DE-604 Palčik, Mark Ja. Verfasser aut Mathematics and its applications 376 (DE-604)BV008163334 376 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fradkin, Efim S. 1924-1999 Palčik, Mark Ja Conformal quantum field theory in D-dimensions Mathematics and its applications Champs, Théorie quantique des ram Conforme invarianten gtt Conforme veldentheorie gtt Hilbertruimten gtt Kwantumveldentheorie gtt Conformal invariants Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4312574-8 |
| title | Conformal quantum field theory in D-dimensions |
| title_auth | Conformal quantum field theory in D-dimensions |
| title_exact_search | Conformal quantum field theory in D-dimensions |
| title_full | Conformal quantum field theory in D-dimensions by Efim S. Fradkin and Mark Ya. Palchik |
| title_fullStr | Conformal quantum field theory in D-dimensions by Efim S. Fradkin and Mark Ya. Palchik |
| title_full_unstemmed | Conformal quantum field theory in D-dimensions by Efim S. Fradkin and Mark Ya. Palchik |
| title_short | Conformal quantum field theory in D-dimensions |
| title_sort | conformal quantum field theory in d dimensions |
| topic | Champs, Théorie quantique des ram Conforme invarianten gtt Conforme veldentheorie gtt Hilbertruimten gtt Kwantumveldentheorie gtt Conformal invariants Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd |
| topic_facet | Champs, Théorie quantique des Conforme invarianten Conforme veldentheorie Hilbertruimten Kwantumveldentheorie Conformal invariants Quantum field theory Quantenfeldtheorie Konforme Feldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT fradkinefims conformalquantumfieldtheoryinddimensions AT palcikmarkja conformalquantumfieldtheoryinddimensions |