The Skyrme model: fundamentals, methods, applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer
1993
|
| Schriftenreihe: | Springer series in nuclear and particle physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 265 S. graph. Darst. |
| ISBN: | 3540549056 0387549056 |
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| 100 | 1 | |a Machankov, Vladimir G. |e Verfasser |4 aut | |
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| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest |b Springer |c 1993 | |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
INTRODUCTION . 1
PART I FUNDAMENTALS
1. THE EVOLUTION OF SKYRME'S APPROACH . 11
1.1 THE "MESONIC FLUID" MODEL . 11
1.2 THE CHIRAL MODIFICATION . 13
1.3 THE TWO-DIMENSIONAL SIMPLIFIED (SINE-GORDON) MODEL . 16
1.3.1 THE IDEA OF TOPOLOGICAL CHARGE . 17
1.3.2 THE ABELIAN BOSONIZATION OR FERMI-BOSE
CORRESPONDENCE . 19
1.4 THE BARYON MODEL - TOPOLOGICAL SKYRMIONS . 21
1.4.1 THE (3+L)-DIMENSIONAL "ANGULAR" VARIABLES . 21
1.4.2 THE TOPOLOGICAL CHARGE IN THE (3+1) MODEL . 23
1.4.3. THE SKYRME MODEL DYNAMICS . 24
1.5 SKYRME'S RESULTS AND CONJECTURES . 27
2. ELEMENTS OF FIELD THEORY WITH TOPOLOGICAL CHARGES
. 30
2.1 GEOMETRIC VIEWPOINT ON THE CLASSICAL FIELD THEORY . 30
2.1.1 THE CONFIGURATION SPACE . 31
2.1.2 HOMOTOPY AS A FORMALIZATION OF DYNAMICAL EVOLUTION 33
2.2 THE TOPOLOGICAL CLASSIFICATION OF SOLUTIONS . 36
2.2.1 HOMOTOPY CLASSES OF THE SINE-GORDON MODEL . 36
2.2.2 THE FUNDAMENTAL AND HIGHER HOMOTOPY GROUPS . 38
2.3 ISHAM'S CONSTRUCTION OF TOPOLOGICAL CHARGES . 40
2.3.1 COHOMOLOGY - HOMOTOPY RELATIONSHIP IN BRIEF . 40
2.3.2 DERIVATION OF TOPOLOGICAL CHARGE
IN THE SKYRME MODEL . 42
2.4 GUIDING PRINCIPLES IN THE CHOICE OF MODEL LAGRANGIANS . 45
2.4.1 CHIRALLY INVARIANT LAGRANGIANS . 46
3. TOPOLOGICAL STABILITY . 49
3.1 SOME GENERAL REMARKS . 49
3.2 THE HOBART-DERRICK THEOREM . 52
3.3 SOLITON STABILITY AND THE SECOND VARIATION STRUCTURE
OF THE LYAPUNOV FUNCTIONAL . 55
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/930223357
XVI
CONTENTS
3.3.1 THE LYAPUNOV STABILITY OF SOLITONS . 55
3.3.2 THE GENERALIZED HOBART-DERRICK THEOREM . 57
3.3.3 THE Q-STABILITY OF SOLITONS . 59
3.4 THE TOPOLOGICAL STABILITY OF SKYRMIONS . 63
PART II METHODS FOR THE STUDY OF SKYRMIONS
4. THE PRINCIPLE OF SYMMETRIC CRITICALITY . 67
4.1 SOME AUXILIARY INFORMATION . 67
4.2 THE SYMMETRY GROUP OF THE SKYRME ENERGY FUNCTIONAL . 69
4.3 THE COLEMAN-PALAIS THEOREM . 72
4.4 THE STRUCTURE OF INVARIANT FIELDS (ANSATZE) . 77
5. ABSOLUTE MINIMUM OF THE ENERGY FUNCTIONAL . 80
5.1 METHOD OF EXTENDING THE PHASE SPACE . 80
5.2 THE SPHERICAL REARRANGEMENT METHOD . 84
5.3 SKYRMION AS THE ABSOLUTE MINIMIZER OF THE ENERGY . 86
6. THE EXISTENCE OF SKYRMIONS . 89
6.1 THE FIELD EQUATIONS FOR SKYRMIONS . 89
6.2 THE DIRECT METHOD IN THE CALCULUS OF VARIATIONS . 92
6.3 AN OUTLINE OF THE PROOF OF THE SKYRMION EXISTENCE . 94
7. MULTI-BARYON AND ROTATING SKYRMION STATES . 99
7.1 THE PROBLEM OF BOUND STATES AND INTERACTION
AMONG SKYRMIONS . 99
7.1.1 THE INVARIANT FIELDS IN HIGHER HOMOTOPY CLASSES . 102
7.2 MINIMA OF THE ENERGY FUNCTIONAL IN HIGHER
HOMOTOPY CLASSES . 104
7.3 THE ROTATING SKYRMION . 109
8. QUANTIZATION OF SKYRMIONS . 113
8.1 BOGOLUBOV'S METHOD OF COLLECTIVE COORDINATES . 114
8.2 CANONICAL QUANTIZATION OF SKYRMIONS . 116
8.3 THE "NON-RIGID" QUANTIZATION OF SKYRMIONS . 120
PART III HADRON PHYSICS APPLICATIONS
9. THE SKYRME MODEL AND QCD . 127
9.1 EXPRESS REVIEW OF THE QCD PRESENT STATUS . 127
9.2 1/FV-EXPANSION . 131
9.3 EFFECTIVE MESON THEORY FROM QCD . 137
9.3.1 THE LOW-ENERGY QCD ATTRIBUTES . 138
9.3.2 THE TOPOLOGICAL CHARGE AS THE BARYON NUMBER . 140
9.3.3 EFFECTIVE CHIRAL LAGRANGIANS FROM QCD . 142
CONTENTS
XVII
10. SKYRNIION AS A FERMION . 147
10.1 THE FINKELSTEIN'S DOUBLE-VALUED FUNCTIONALS . 147
10.2 THE CHARGE-MONOPOLE MULTI-VALUED ACTION . 152
10.3 THE WESS-ZUMINO TERM AND WITTEN'S REALIZATION
OF SKYRME'S SUGGESTION . 155
10.3.1 THE WESS-ZUMINO TERM IN EFFECTIVE CHIRAL
LAGRANGIAN . 157
10.3.2 SPIN AND STATISTICS OF SKYRMIONS . 160
11.
QUANTIZED SU(Z) SKYRMIONS AND THEIR INTERACTIONS . 164
11.1 THE SU(Z) GENERALIZED LAGRANGIAN IN TERMS
OF COLLECTIVE COORDINATES . 164
11.1.1 THE SU(3) SKYRME "COLLECTIVE" LAGRANGIAN . 165
11.1.2 THE WESS-ZUMINO TERM FOR COLLECTIVE COORDINATES . 166
11.1.3 THE SYMMETRY BREAKING TERM . 168
11.2 QUANTIZATION IN THE PRESENCE OF THE WESS-ZUMINO TERM . 171
11.2.1 CANONICAL QUANTIZATION . 171
11.2.2 SYMMETRIES, CONSTRAINT AND SPECTRUM . 173
11.2.3 STATIC OBSERVABLES AND MASS FORMULAE . 178
11.3 SKYRMIONS' INTERACTIONS: NUCLEAR FORCES
AND NUCLEAR MATTER . 181
11.3.1 THE SKYRMION-SKYRMION INTERACTION AND
NUCLEAR FORCES . 182
11.3.2 THE MESON-BARYON INTERACTION . 184
11.3.3 THE SKYRME MODEL AND NUCLEAR MATTER . 187
CONCLUDING REMARKS . 192
PART IV APPENDICES
A. CHIRAL SYMMETRY . 197
A.L ALGEBRAIC ASPECTS OF CHIRAL SYMMETRY . 198
A. 2 GEOMETRIC ASPECTS OF CHIRAL SYMMETRY . 200
B. A CONCISE ACCOUNT OF ALGEBRAIC TOPOLOGY
. 204
B. L SMOOTH MANIFOLDS . 204
B.2 TANGENT SPACES, VECTOR FIELDS AND LIE ALGEBRAS . 208
B.3 DIFFERENTIAL FORMS . 212
B.4 INTEGRATION ON MANIFOLDS AND DE RHAM CO-HOMOLOGIES . 217
B. 5 FUNDAMENTAL GROUPS, HOMOTOPY GROUPS AND SOME
OTHER TOPOLOGICAL INVARIANTS . 221
C.
METHODS OF REDUCTION . 229
C. L REDUCTION TO STATIC FIELD CONFIGURATIONS . 229
C.2 REDUCTION TO G-INVARIANT FIELDS . 230
C.3 SPHERICAL REARRANGEMENT TECHNIQUE: AN ILLUSTRATION . 232
XVIII
CONTENTS
D. PROOFS OF STABILITY AND EXISTENCE THEOREMS . 234
D.L PROOF OF GENERALIZED HOBART-DERRICK THEOREM . 234
D.2 EXISTENCE OF THE AXIALLY-SYMMETRIC SOLUTIONS . 236
D.3 EXISTENCE OF A NONSINGULAR MATRIX . 238
E. FINKELSTEIN-WILLIAMS' SPINOR STRUCTURES . 239
REFERENCES . 243
SUBJECT INDEX . 261 |
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| author | Machankov, Vladimir G. Rybakov, Jurij P. 1939- Sanjuk, Valerij I. 1950- |
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| spelling | Machankov, Vladimir G. Verfasser aut The Skyrme model fundamentals, methods, applications V. G. Makhankov ; Y. P. Rybakov ; V. I. Sanyuk Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer 1993 XVIII, 265 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in nuclear and particle physics Chirale Symmetrie (DE-588)4274371-0 gnd rswk-swf Skyrmion-Modell (DE-588)4242058-1 gnd rswk-swf Quantenchromodynamik (DE-588)4128082-9 gnd rswk-swf Skyrmion-Modell (DE-588)4242058-1 s DE-604 Quantenchromodynamik (DE-588)4128082-9 s Chirale Symmetrie (DE-588)4274371-0 s Rybakov, Jurij P. 1939- Verfasser (DE-588)135974372 aut Sanjuk, Valerij I. 1950- Verfasser (DE-588)135974410 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Machankov, Vladimir G. Rybakov, Jurij P. 1939- Sanjuk, Valerij I. 1950- The Skyrme model fundamentals, methods, applications Chirale Symmetrie (DE-588)4274371-0 gnd Skyrmion-Modell (DE-588)4242058-1 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| subject_GND | (DE-588)4274371-0 (DE-588)4242058-1 (DE-588)4128082-9 |
| title | The Skyrme model fundamentals, methods, applications |
| title_auth | The Skyrme model fundamentals, methods, applications |
| title_exact_search | The Skyrme model fundamentals, methods, applications |
| title_full | The Skyrme model fundamentals, methods, applications V. G. Makhankov ; Y. P. Rybakov ; V. I. Sanyuk |
| title_fullStr | The Skyrme model fundamentals, methods, applications V. G. Makhankov ; Y. P. Rybakov ; V. I. Sanyuk |
| title_full_unstemmed | The Skyrme model fundamentals, methods, applications V. G. Makhankov ; Y. P. Rybakov ; V. I. Sanyuk |
| title_short | The Skyrme model |
| title_sort | the skyrme model fundamentals methods applications |
| title_sub | fundamentals, methods, applications |
| topic | Chirale Symmetrie (DE-588)4274371-0 gnd Skyrmion-Modell (DE-588)4242058-1 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| topic_facet | Chirale Symmetrie Skyrmion-Modell Quantenchromodynamik |
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