Path integrals in field theory: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Advanced texts in physics
Physics and astronomy online library |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 213 S. graph. Darst. |
| ISBN: | 3540403825 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | ULRICH MOSEL PATH INTEGRALS IN FIELD THEORY AN INTRODUCTION WITH 19
FIGURES SPRINGER CONTENTS PART I NON-RELATIVISTIC QUANTUM THEORY THE
PATH INTEGRAL IN QUANTUM THEORY 3 1.1 PROPAGATOR OF THE SCHRODINGER
EQUATION 3 1.2 PROPAGATOR AS PATH INTEGRAL 5 1.3 QUADRATIC HAMILTONIANS
9 1.3.1 CARTESIAN METRIC 9 1.3.2 NON-CARTESIAN METRIC 11 1.4 CLASSICAL
INTERPRETATION 13 PERTURBATION THEORY 15 2.1 FREE PROPAGATOR 15 2.2
PERTURBATIVE EXPANSION 17 2.3 APPLICATION TO SCATTERING 22 GENERATING
FUNCTIONALS 27 3.1 GROUNDSTATE-TO-GROUNDSTATE TRANSITIONS 27 3.1.1
GENERATING FUNCTIONAL 31 3.2 FUNCTIONAL DERIVATIVES OF GS-GS TRANSITION
AMPLITUDES 32 PART II RELATIVISTIC QUANTUM FIELD THEORY RELATIVISTIC
FIELDS 39 4.1 EQUATIONS OF MOTION 39 4.1.1 EXAMPLES 41 4.2 SYMMETRIES
AND CONSERVATION LAWS 46 4.2.1 GEOMETRICAL SPACE*TIME SYMMETRIES 47
4.2.2 INTERNAL SYMMETRIES 49 PATH INTEGRALS FOR SCALAR FIELDS 53 5.1
GENERATING FUNCTIONAL FOR FIELDS 53 5.1.1 EUCLIDEAN REPRESENTATION 56 X
CONTENTS 6 EVALUATION OF PATH INTEGRALS 59 6.1 FREE SCALAR FIELDS 59
6.1.1 GENERATING FUNCTIONAL 59 6.1.2 FEYNMAN PROPAGATOR 61 6.1.3
GAUSSIAN INTEGRATION 64 6.2 INTERACTING SCALAR FIELDS 67 6.2.1
STATIONARY PHASE APPROXIMATION 67 6.2.2 NUMERICAL EVALUATION OF PATH
INTEGRALS 70 6.2.3 REAL TIME FORMALISM 72 7 TRANSITION RATES AND GREEN S
FUNCTIONS 75 7.1 SCATTERING MATRIX 75 7.2 REDUCTION THEOREM 77 7.2.1
CANONICAL FIELD QUANTIZATION 77 7.2.2 DERIVATION OF THE REDUCTION
THEOREM 78 8 GREEN S FUNCTIONS 85 8.1 N-POINT GREEN S FUNCTIONS 85 8.1.1
MOMENTUM REPRESENTATION 86 8.1.2 OPERATOR REPRESENTATIONS 86 8.2 FREE
SCALAR FIELDS 89 8.2.1 WICK S THEOREM 89 8.2.2 FEYNMAN RULES 91 8.3
INTERACTING SCALAR FIELDS 92 8.3.1 PERTURBATIVE EXPANSION 93 9
PERTURBATIVE 4 4 THEORY 97 9.1 PERTURBATIVE EXPANSION OF THE GENERATING
FUNCTION 97 9.1.1 GENERATING FUNCTIONAL UP TO O{G) 98 9.2 TWO-POINT
FUNCTION 101 9.2.1 TERMS UP TO O{G) 101 9.2.2 TERMS UP TO O{G) 102
9.2.3 TERMS UP TO O{G 2 ) 104 9.3 FOUR-POINT FUNCTION 106 9.3.1 TERMS UP
TO O(G) 106 9.3.2 TERMS UP TO O(G 2 ) 107 9.4 DIVERGENCES IN N-POINT
FUNCTIONS 110 9.4.1 POWER COUNTING 110 9.4.2 DIMENSIONAL REGULARIZATION
OF / 4 THEORY 113 9.4.3 RENORMALIZATION 119 CONTENTS XI 10 GREEN S
FUNCTIONS FOR FERMIONS 125 10.1 GRASSMANN ALGEBRA 125 10.1.1 DERIVATIVES
126 10.1.2 INTEGRATION 128 10.2 GREEN S FUNCTIONS FOR FERMIONS 134
10.2.1 GENERATING FUNCTIONAL FOR FERMIONS 134 10.2.2 REDUCTION THEOREM
FOR FERMIONS 138 10.2.3 GREEN S FUNCTIONS 139 11 INTERACTING FIELDS 141
11.1 FEYNMAN RULES 141 11.1.1 FERMION LOOPS 143 11.2 WICK S THEOREM 145
11.3 BOSONIZATION OF YUKAWA THEORY 147 11.3.1 PERTURBATIVE EXPANSION 150
PART III GAUGE FIELD THEORY 12 PATH INTEGRALS FOR QED 157 12.1 GAUGE
INVARIANCE IN ABELIAN FREE FIELD THEORIES 157 12.2 GENERATING FUNCTIONAL
161 12.3 GAUGE INVARIANCE IN QED 162 12.4 FEYNMAN RULES OF QED 164 13
PATH INTEGRALS FOR GAUGE FIELDS 167 13.1 NON-ABELIAN GAUGE FIELDS 167
13.2 GENERATING FUNCTIONAL 171 13.3 GAUGE FIXING OF 176 13.4
FADDEEV-POPOV DETERMINANT 178 13.4.1 EXPLICIT FORMS OF THE FP
DETERMINANT 180 13.4.2 GHOST FIELDS 182 13.5 FEYNMAN RULES 184 14
EXAMPLES FOR GAUGE FIELD THEORIES 189 14.1 QUANTUM CHROMODYNAMICS 189
14.2 ELECTROWEAK INTERACTIONS 190 UNITS AND METRIC 193 A.I UNITS 193 A.2
METRIC AND NOTATION 194 XII CONTENTS FUNCTIONALS 197 B.I DEFINITION 197
B.2 FUNCTIONAL INTEGRATION 197 B.2.1 GAUSSIAN INTEGRALS 198 B.3
FUNCTIONAL DERIVATIVES 201 RENORMALIZATION INTEGRALS 203 GAUSSIAN
GRASSMANN INTEGRATION 207 REFERENCES 209 INDEX 211
|
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| author | Mosel, Ulrich 1943- |
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| callnumber-subject | QC - Physics |
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| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3 |
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| discipline | Physik Mathematik |
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| indexdate | 2024-07-09T19:18:41Z |
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| isbn | 3540403825 |
| language | English |
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| spelling | Mosel, Ulrich 1943- Verfasser (DE-588)106321412 aut Path integrals in field theory an introduction Ulrich Mosel Berlin [u.a.] Springer 2004 XII, 213 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced texts in physics Physics and astronomy online library Champs, Théorie quantique des Intégrales de parcours Kwantumveldentheorie gtt Natuurkunde gtt Pad-integralen gtt Physik Path integrals Quantum field theory Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Pfadintegral (DE-588)4173973-5 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mosel, Ulrich 1943- Path integrals in field theory an introduction Champs, Théorie quantique des Intégrales de parcours Kwantumveldentheorie gtt Natuurkunde gtt Pad-integralen gtt Physik Path integrals Quantum field theory Pfadintegral (DE-588)4173973-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4173973-5 (DE-588)4047984-5 |
| title | Path integrals in field theory an introduction |
| title_auth | Path integrals in field theory an introduction |
| title_exact_search | Path integrals in field theory an introduction |
| title_full | Path integrals in field theory an introduction Ulrich Mosel |
| title_fullStr | Path integrals in field theory an introduction Ulrich Mosel |
| title_full_unstemmed | Path integrals in field theory an introduction Ulrich Mosel |
| title_short | Path integrals in field theory |
| title_sort | path integrals in field theory an introduction |
| title_sub | an introduction |
| topic | Champs, Théorie quantique des Intégrales de parcours Kwantumveldentheorie gtt Natuurkunde gtt Pad-integralen gtt Physik Path integrals Quantum field theory Pfadintegral (DE-588)4173973-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Champs, Théorie quantique des Intégrales de parcours Kwantumveldentheorie Natuurkunde Pad-integralen Physik Path integrals Quantum field theory Pfadintegral Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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