Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-260298 Inhaltsverzeichnis |
| Physical Description: | IV, 127 S. graph. Darst. |
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MARC
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Record in the Search Index
| _version_ | 1804149531517911040 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1. THE STANDARD MODEL 1
1.2. THE QUARK MODEL 2
1.3. UNIT CONVENTION 4
2. QUANTUM CHROMODYNAMICS ON T H E LATTICE 5
2.1. QCD IN THE CONTINUUM - A REVIEW 5
2.1.1. THE EUCLIDEAN TIME 5
2.1.2. THE FERMIONIC LAGRANGIAN 6
2.1.3. THE GAUGE PART OF THE LAGRANGIAN 9
2.2. THE LATTICE DISCRETISATION 10
2.2.1. DISCRETISING THE FREE FERMION ACTION 11
2.2.2. INTRODUCING GAUGE FIELDS 12
2.2.3. THE LATTICE GAUGE ACTION 14
2.3. WILSON FERMIONS 16
2.3.1. THE DIRAC OPERATOR 16
2.3.2. FERMION DOUBLING IT
2.3.3. WILSON FERMION ACTION 19
2.3.4. CLOVER IMPROVEMENT 20
3. T H E PATH INTEGRAL ON T H E LATTICE 2 1
3.1. THE EUCLIDEAN CORRELATOR 21
3.2. CALCULATING THE PATH INTEGRAL 23
3.3. NUMERICAL EVALUATION OF THE PATH INTEGRAL 25
3.3.1. MONTE CARLO INTEGRATION 25
3.3.2. MARKOV CHAINS AND METROPOLIS ALGORITHM 26
4. MESONS ON T H E LATTICE 29
4.1. MESON INTERPOLATORS 29
4.2. SOURCES AND SMEARING 32
4.3. EXTRACTING ENERGIES 34
4.3.1. GENERAL CONSIDERATIONS 34
4.3.2. THE VARIATIONAL METHOD 35
4.4. SETTING THE SCALE 36
III
HTTP://D-NB.INFO/1028840438
IMAGE 2
CONTENTS
5. RESONANCE SCATTERING ON T H E LATTICE 39
5.1. DERIVATION OF THE PHASE SHIFT FORMULA 40
6. DETERMINATION O F T H E SCATTERING PHASE SHIFT FOR NON-ZERO TOTAL
MOMENTA 47 6.1. GROUP THEORY 47
6.2. SCATTERING PHASES 48
7. OPERATORS FOR PION RESONANCE SCATTERING AND THEIR TRANSFORMATION
BEHAVIOUR UNDER POINT GROUPS 5 3
7.1. OPERATORS FOR PION SCATTERING 53
7.2. TRANSFORMATION OF 2-PARTICLE OPERATORS 54
7.2.1. TRANSFORMATION UNDER D,U, -56
7.2.2. TRANSFORMATION UNDER DIH 59
7.2.3. TRANSFORMATION UNDER D M 60
7.3. THE RHO MESON OPERATOR 62
7.3.1. TRANSFORMATION UNDER L) IK 63
7.3.2. TRANSFORMATION UNDER D ^ 64
7.3.3. TRANSFORMATION UNDER D U * 64
8. ENERGY LEVELS FROM RESONANCE SCATTERING 67
5.1. THE EFFECTIVE RANGE MODEL 67
8.2. THE 2-PION OPERATORS 68
8.2.1. GROUP UIH 68
8.2.2. GROUP D-M 69
8.2.3. GROUP 71
8.3. ENERGY LEVEL PLOTS 71
9. T H E CORRELATION FUNCTIONS 77
9.1. THE 2-PION CORRELATION FUNCTION 77
9.2. THE REMAINING CORRELATION FUNCTIONS 83
10. RESULTS 87
10.1. RESULTS AND DISCUSSION 87
10.2. SUMMARY AND OUTLOOK 92
A. CALCULATION O F T H E GENERALISED ZETA FUNCTION 99
A.L. GENERAL FORMALISM 99
A.2. DERIVATION FOR D 4/,. DON AND D M 101
B. T H E JACKKNIFE METHOD 107
C. ENERGY AND PHASE SHIFT TABLES 109
IV
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| physical | IV, 127 S. graph. Darst. |
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| spelling | Gutzwiller, Simone Verfasser (DE-588)1028840187 aut Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD vorgelegt von Simone Gutzwiller 2012 IV, 127 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regensburg, Univ., Diss., 2012 Quantenchromodynamik (DE-588)4128082-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantenchromodynamik (DE-588)4128082-9 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:355-epub-260298 http://epub.uni-regensburg.de/26029/ Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-260298 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025314867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gutzwiller, Simone Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD Quantenchromodynamik (DE-588)4128082-9 gnd |
| subject_GND | (DE-588)4128082-9 (DE-588)4113937-9 |
| title | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD |
| title_auth | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD |
| title_exact_search | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD |
| title_full | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD vorgelegt von Simone Gutzwiller |
| title_fullStr | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD vorgelegt von Simone Gutzwiller |
| title_full_unstemmed | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD vorgelegt von Simone Gutzwiller |
| title_short | Scattering phase shift for elastic two pion scattering and the rho resonance in lattice QCD |
| title_sort | scattering phase shift for elastic two pion scattering and the rho resonance in lattice qcd |
| topic | Quantenchromodynamik (DE-588)4128082-9 gnd |
| topic_facet | Quantenchromodynamik Hochschulschrift |
| url | http://epub.uni-regensburg.de/26029/ https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-260298 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025314867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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