Spectral methods in quantum field theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in physics
777 |
| Subjects: | |
| Online Access: | Cover Vorwort 1 Kapitel 1 Inhaltsverzeichnis |
| Physical Description: | XI, 182 S. graph. Darst. |
| ISBN: | 9783642001383 9783642001390 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 1 1.1 BACKGROUND AND
MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 INVITATION: A SAMPLE CALCULATION . . . . . . . . . . . . . . . . . .
. . . . . . . 3 1.2.1 ZERO-POINT ENERGIES: SUMMING 1 2 * * . . . . . . .
. . . . . . . . . . 3 1.2.2 FROM DISCRETE TO CONTINUOUS: PHASE SHIFTS
AND THE DENSITY OF STATES . . . . . . . . . . . . . . . . . . . . . . .
. . . 5 1.2.3 COUNTING STATES: LEVINSON*S THEOREM . . . . . . . . . . .
. . . . 6 1.2.5 COMPUTATIONAL TECHNIQUES . . . . . . . . . . . . . . . .
. . . . . . . . 11 REFERENCES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 REVIEW OF
SCATTERING THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 15 2.1 SCATTERING THEORY IN ARBITRARY DIMENSION . . . . . . . . . .
. . . . . . . 15 2.2 GREEN*S FUNCTIONS FROM SCATTERING DATA . . . . . .
. . . . . . . . . . . . . 18 2.3 PHASE SHIFTS AND DENSITY OF STATES . .
. . . . . . . . . . . . . . . . . . . . . . 20 2.4 LEVINSON*S THEOREM
AND FINITE ENERGY SUM RULES . . . . . . . . . . 23 2.4.1 OVERVIEW AND
SIMPLIFIED DERIVATION . . . . . . . . . . . . . . . . . 24 2.4.3 THE
SYMMETRIC CHANNEL IN ONE DIMENSION . . . . . . . . . . 29 REFERENCES . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 32 3 QUANTUM FIELD THEORY AND THE SPECTRAL METHOD
. . . . . . . . . 33 3.1 SMALL-AMPLITUDE QUANTUM CORRECTIONS. . . . . .
. . . . . . . . . . . . . . 33 3.2 THE CANONICAL FORMALISM . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 THE VACUUM
ENERGY DENSITY . . . . . . . . . . . . . . . . . . . . . . 35 3.2.2 THE
VACUUM ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 40 3.3 THE PATH INTEGRAL APPROACH . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 41 3.4 CONNECTING THE FUNCTIONAL AND CANONICAL
FORMALISMS . . . . . . . 43 3.5 FEYNMAN DIAGRAMS AND THE BORN SERIES . .
. . . . . . . . . . . . . . . . . 44 3.6 SOME REMARKS ON RENORMALIZATION
. . . . . . . . . . . . . . . . . . . . . . . 52 3.7 QUANTUM ENERGY OF
INTERFACES. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 60 X CONTENTS 4 APPLICATIONS IN ONE
SPACE DIMENSION . . . . . . . . . . . . . . . . . . . . . 63 4.1 VACUUM
POLARIZATION ENERGY IN EXACTLY SOLVABLE MODELS . . . . 63 4.2 FERMIONS
IN ONE SPATIAL DIMENSION . . . . . . . . . . . . . . . . . . . . . . .
67 4.2.1 PARITY-INVARIANT BACKGROUND FIELDS . . . . . . . . . . . . . .
. . . 67 4.2.2 FERMIONS IN THE SINE-GORDON BACKGROUND . . . . . . . . .
. . . 70 4.2.3 FERMIONS IN THE KINK BACKGROUND . . . . . . . . . . . . .
. . . . . 72 4.3 BOSONS, FERMIONS, SUPERSYMMETRY, CENTRAL CHARGE, AND
THE BPS BOUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 76 4.3.1 FERMIONS . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3.2
SUPERSYMMETRY AND CENTRAL CHARGE . . . . . . . . . . . . . . . . 77
4.3.3 SVV ANOMALY . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 81 4.4 SOLITON STABILIZATION BY FERMIONS IN D = 1+1. . .
. . . . . . . . . . . . 82 4.4.1 THE ONE-LOOP EFFECTIVE ENERGY . . . . .
. . . . . . . . . . . . . . . 85 4.4.2 THE FERMION NUMBER . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 86 4.4.3 RESULTS. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 88 5 SPECTRAL ANALYSIS OF
CHARGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.1
BASIC IDEA AND DERIVATION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 91 5.2 ELECTROSTATICS AND THE NEED FOR REGULARIZATION .
. . . . . . . . . . . . 93 5.3 CHIRAL BAG MODEL IN ONE SPACE DIMENSION .
. . . . . . . . . . . . . . . 96 5.4 CHIRAL BAG MODEL IN THREE SPACE
DIMENSIONS . . . . . . . . . . . . . . 97 REFERENCES . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 101 6 HEDGEHOG CONFIGURATIONS IN D = 3 + 1 . . . . . . . . . . . .
. . . . . . . . 103 6.1 CHIRAL FERMIONS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 103 6.1.1 THE MODEL . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103 6.1.2 THE FERMION LOOP. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 104 6.1.3 NUMERICAL ANALYSIS . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 110 6.2 SU L (2) GAUGE THEORY . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.2.1
CLASSICAL SPHALERONS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 117 6.2.2 ENERGETICALLY STABILIZED SOLITONS . . . . . . . . . .
. . . . . . . . . . 119 6.2.3 THE SEARCH FOR THE SOLITON . . . . . . . .
. . . . . . . . . . . . . . . . . 120 6.2.4 BEYOND THE SPHERICAL ANSATZ.
. . . . . . . . . . . . . . . . . . . . . . 127 REFERENCES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 127 7 BOUNDARY CONDITIONS AND CASIMIR FORCES . . . . . . . .
. . . . . . . . . 129 7.1 DIRICHLET CONDITIONS FROM QUANTUM FIELD
THEORY. . . . . . . . . . . 131 7.2 RIGID BODIES: DIRICHLET POINTS AND
PARALLEL PLATES . . . . . . . . . . . 132 7.3 THE CASIMIR STRESS ON A
DIRICHLET RING . . . . . . . . . . . . . . . . . . . . 136 7.4
OVERSUBTRACTION AND DIAGRAMMATIC ANALYSIS . . . . . . . . . . . . . . .
139 7.5 THE DIRICHLET SPHERE . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 140 REFERENCES . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
CONTENTS XI 8 STRING-TYPE CONFIGURATIONS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 143 8.1 FLUX TUBES IN QUANTUM
ELECTRODYNAMICS . . . . . . . . . . . . . . . . . . 143 8.1.1 THE VORTEX
CONFIGURATION . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.1.2 THE QUANTUM ENERGY OF THE VORTEX . . . . . . . . . . . . . . . .
144 8.1.3 SUBTLETIES OF CONFIGURATIONS WITH NET FLUX AND EMBEDDING . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
146 8.1.4 NUMERICAL RESULTS FOR THE QUANTUM ENERGY. . . . . . . . . .
148 8.1.5 QUANTUM ENERGY DENSITY . . . . . . . . . . . . . . . . . . . .
. . . . . 151 8.2 FLUX TUBES AND STRINGS IN THE ELECTROWEAK STANDARD
MODEL . . 153 8.2.1 THE BOSONIC SECTOR . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 154 8.2.2 THE STRING SOLUTIONS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 155 8.2.3 THE SPHALERON
SQUARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.2.4
THE FERMION ACTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 157 8.2.5 FERMIONS ON STRINGS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 158 8.2.6 THE VACUUM POLARIZATION ENERGY . . . .
. . . . . . . . . . . . . . . 159 8.2.7 NUMERICAL RESULTS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 163 REFERENCES . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 168 9 QUANTUM CORRECTIONS TO Q -BALLS . . . . . . . .
. . . . . . . . . . . . . . . . . . 171 9.1 THE Q -BALL . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171 9.2 QUANTUM CORRECTIONS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 173 9.3 APPLICATIONS . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 177 INDEX . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 179
|
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| id | DE-604.BV035581080 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:40:55Z |
| institution | BVB |
| isbn | 9783642001383 9783642001390 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017636497 |
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| physical | XI, 182 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | Springer |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Graham, Noah Verfasser (DE-588)138224277 aut Spectral methods in quantum field theory N. Graham ; M. Quandt ; H. Weigel Berlin [u.a.] Springer 2009 XI, 182 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 777 Perturbation (Quantum dynamics) Quantum field theory Scattering (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Streutheorie (DE-588)4183697-2 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Streutheorie (DE-588)4183697-2 s DE-604 Quandt, Markus 1967- Verfasser (DE-588)121305988 aut Weigel, Herbert Verfasser aut Lecture notes in physics 777 (DE-604)BV000003166 777 DE-576;springer image/jpeg http://swbplus.bsz-bw.de/bsz306928914cov.htm 20090527201026 Cover DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz306928914vor.htm 20090528030402 Vorwort 1 DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz306928914kap.htm 20090528030359 Kapitel 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017636497&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graham, Noah Quandt, Markus 1967- Weigel, Herbert Spectral methods in quantum field theory Lecture notes in physics Perturbation (Quantum dynamics) Quantum field theory Scattering (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4183697-2 |
| title | Spectral methods in quantum field theory |
| title_auth | Spectral methods in quantum field theory |
| title_exact_search | Spectral methods in quantum field theory |
| title_full | Spectral methods in quantum field theory N. Graham ; M. Quandt ; H. Weigel |
| title_fullStr | Spectral methods in quantum field theory N. Graham ; M. Quandt ; H. Weigel |
| title_full_unstemmed | Spectral methods in quantum field theory N. Graham ; M. Quandt ; H. Weigel |
| title_short | Spectral methods in quantum field theory |
| title_sort | spectral methods in quantum field theory |
| topic | Perturbation (Quantum dynamics) Quantum field theory Scattering (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Perturbation (Quantum dynamics) Quantum field theory Scattering (Physics) Quantenfeldtheorie Streutheorie |
| url | http://swbplus.bsz-bw.de/bsz306928914cov.htm http://swbplus.bsz-bw.de/bsz306928914vor.htm http://swbplus.bsz-bw.de/bsz306928914kap.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017636497&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT grahamnoah spectralmethodsinquantumfieldtheory AT quandtmarkus spectralmethodsinquantumfieldtheory AT weigelherbert spectralmethodsinquantumfieldtheory |