Graph theory and Feynman integrals:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Gordon & Breach
1971
|
| Series: | Mathematics and its applications
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 223 S. |
| ISBN: | 0677029500 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV005707616 | ||
| 003 | DE-604 | ||
| 005 | 20220504 | ||
| 007 | t | ||
| 008 | 921028s1971 |||| 00||| eng d | ||
| 020 | |a 0677029500 |9 0-677-02950-0 | ||
| 035 | |a (OCoLC)136501 | ||
| 035 | |a (DE-599)BVBBV005707616 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-739 |a DE-355 |a DE-20 |a DE-384 |a DE-19 |a DE-91 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA166 | |
| 082 | 0 | |a 539.7/21 |2 18 | |
| 082 | 0 | |a 515/.43 | |
| 084 | |a QH 400 |0 (DE-625)141571: |2 rvk | ||
| 084 | |a SK 170 |0 (DE-625)143221: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a UO 2000 |0 (DE-625)146210: |2 rvk | ||
| 084 | |a PHY 013f |2 stub | ||
| 100 | 1 | |a Nakanishi, Noboru |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Graph theory and Feynman integrals |c Noboru Nakanishi |
| 264 | 1 | |a New York |b Gordon & Breach |c 1971 | |
| 300 | |a XI, 223 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 11 | |
| 650 | 7 | |a Feynman-integralen |2 gtt | |
| 650 | 7 | |a Grafen |2 gtt | |
| 650 | 4 | |a Graphes, Théorie des | |
| 650 | 4 | |a Intégrales | |
| 650 | 4 | |a Feynman integrals | |
| 650 | 4 | |a Graph theory | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Pfadintegral |0 (DE-588)4173973-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Pfadintegral |0 (DE-588)4173973-5 |D s |
| 689 | 0 | 1 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Mathematics and its applications |v 11 |w (DE-604)BV008163334 |9 11 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003565494 | ||
Record in the Search Index
| _version_ | 1804119894168436736 |
|---|---|
| adam_text | Contents
PREFACE vii
CHAPTER 1 GRAPH THEORY 1
§ 1 Terminology and Notation 3
1 1 Set theoretical concepts 3
1 2 Graphs 4
1 3 Paths, circuits, cut sets, trees 7
1 4 Feynman graphs 8
§ 2 Fundamental Properties of a Graph ...... 10
2 1 Properties independent of orientation 10
2 2 Fundamental sets of circuits and cut sets 14
2 3 Duality 20
§3 Matrices and Topological Formulas . . . . . . 21
3 1 Matrices associated with a graph 21
3 2 Topological formulas 24
§ 4 Planar Graphs 32
4 1 Characterizations of the planar graph 32
4 2 Dual graphs 33
§ 5 Transport Problem 37
References 43
CHAPTER 2 FEYNMAN PARAMETRIC FORMULA .... 44
§ 6 Feynman Integral 46
6 1 Physical background 46
6 2 Definition of the Feynman Integral 52
§ 7 FeynmOn Parametric Integral ....... 56
7 1 Derivation of the Feynman parametric integral 56
7 2 Topological formulas for the V function 59
7 3 Remarks 64
§ 8 Position Space Approaches ........ 68
8 1 Inverse Feynman parametric integral 68
8 2 Position space Feynman parametric integral 71
ix
X CONTENTS
§ 9 Feynman Parametric Functions ....... 75
9 1 Properties of U and V 75
9 2 Presence of nonzero spin particles 76
§ 10 Ultraviolet Divergence 81
10 1 Proof of Dyson s power counting theorem 81
10 2 Renormalization 84
References 88
CHAPTER 3 SINGULARITIES OF THE FEYNMAN INTEGRAL . . 90
§ 11 Feynman Function 92
§ 12 Landau Singularities ......... 94
12 1 Landau equations 94
12 2 Dual graph analysis 98
12 3 Behavior near the singularity 99
§ 13 Real Singularities 102
13 1 General consideration on real singularities 102
13 2 Normal and anomalous thresholds 105
§ 14 Physical Region Singularities . . . . . . . 112
14 1 Multiple scattering 112
14 2 Discontinuity formula 114
14 3 Infrared Divergence 115
§ 15 Existence Region of Singularities 118
§ 16 Second Type Singularities 122
16 1 Pure second type singularities 122
16 2 Mixed second type singularities 126
References 127
CHAPTER 4 PERTURBATION THEORETICAL INTEGRAL REPRESEN¬
TATIONS 129
§17 Definition of PTIR 131
17 1 General Remarks 131
17 2 Derivation of PTIR 133
17 3 Position space PTIR 139
§18 Mathematical Properties of PTIR 140
18 1 Analyticity 140
18 2 Uniqueness 141
18 3 Other properties 145
CONTENTS Xi
§ 19 Support Properties in the General Mass Case 147
19 1 General Method 147
19 2 Vertex function 149
19 3 Extended scattering amplitude 151
§ 20 Mqjorization Method 158
20 1 Models 158
20 2 Majorization rules 160
20 3 Majorization procedure 165
§21 W Function Inequalities 169
§ 22 Support Properties in Particular Models . . . . . . 175
22 1 Vertex function 175
22 2 Scattering amplitude 176
22 3 Proof of dispersion relations 180
22 4 One particle production amplitude 181
References 182
CHAPTER 5 MISCELLANEOUS TOPICS 183
§ 23 Number ofFeynman Graphs ........ 184
§24 Divergence of the Perturbation Series . . . . . . 189
§ 25 Cut Set Properties ofFeynman Graphs ...... 193
§26 High Energy Asymptotic Behavior of the Feynman Integral . . 196
References 199
APPENDIX A SOME ANALYTICAL CONCEPTS 200
A l Distributions 200
A 2 Analytic functions 203
References 207
APPENDIX B FEYNMAN INTEGRALS FOR SINGLE LOOP GRAPHS . 208
B l General remarks and Self energy 208
B 2 Vertex function 210
B 3 Scattering Amplitude 213
B 4 Production Amplitudes 213
References 215
AUTHOR INDEX 217
SUBJECT INDEX 219
|
| any_adam_object | 1 |
| author | Nakanishi, Noboru |
| author_facet | Nakanishi, Noboru |
| author_role | aut |
| author_sort | Nakanishi, Noboru |
| author_variant | n n nn |
| building | Verbundindex |
| bvnumber | BV005707616 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166 |
| callnumber-search | QA166 |
| callnumber-sort | QA 3166 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 400 SK 170 SK 890 UO 2000 |
| classification_tum | PHY 013f |
| ctrlnum | (OCoLC)136501 (DE-599)BVBBV005707616 |
| dewey-full | 539.7/21 515/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics 515 - Analysis |
| dewey-raw | 539.7/21 515/.43 |
| dewey-search | 539.7/21 515/.43 |
| dewey-sort | 3539.7 221 |
| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01868nam a2200517 cb4500</leader><controlfield tag="001">BV005707616</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220504 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">921028s1971 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0677029500</subfield><subfield code="9">0-677-02950-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)136501</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005707616</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA166</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">539.7/21</subfield><subfield code="2">18</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.43</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 400</subfield><subfield code="0">(DE-625)141571:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UO 2000</subfield><subfield code="0">(DE-625)146210:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 013f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nakanishi, Noboru</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Graph theory and Feynman integrals</subfield><subfield code="c">Noboru Nakanishi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Gordon & Breach</subfield><subfield code="c">1971</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 223 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">11</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Feynman-integralen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Grafen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graphes, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intégrales</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Feynman integrals</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graph theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Pfadintegral</subfield><subfield code="0">(DE-588)4173973-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Pfadintegral</subfield><subfield code="0">(DE-588)4173973-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">11</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">11</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003565494</subfield></datafield></record></collection> |
| id | DE-604.BV005707616 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:26Z |
| institution | BVB |
| isbn | 0677029500 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003565494 |
| oclc_num | 136501 |
| open_access_boolean | |
| owner | DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-384 DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-384 DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-83 DE-188 |
| physical | XI, 223 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Gordon & Breach |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Nakanishi, Noboru Verfasser aut Graph theory and Feynman integrals Noboru Nakanishi New York Gordon & Breach 1971 XI, 223 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 11 Feynman-integralen gtt Grafen gtt Graphes, Théorie des Intégrales Feynman integrals Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 s Graphentheorie (DE-588)4113782-6 s DE-604 Mathematics and its applications 11 (DE-604)BV008163334 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nakanishi, Noboru Graph theory and Feynman integrals Mathematics and its applications Feynman-integralen gtt Grafen gtt Graphes, Théorie des Intégrales Feynman integrals Graph theory Graphentheorie (DE-588)4113782-6 gnd Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4173973-5 |
| title | Graph theory and Feynman integrals |
| title_auth | Graph theory and Feynman integrals |
| title_exact_search | Graph theory and Feynman integrals |
| title_full | Graph theory and Feynman integrals Noboru Nakanishi |
| title_fullStr | Graph theory and Feynman integrals Noboru Nakanishi |
| title_full_unstemmed | Graph theory and Feynman integrals Noboru Nakanishi |
| title_short | Graph theory and Feynman integrals |
| title_sort | graph theory and feynman integrals |
| topic | Feynman-integralen gtt Grafen gtt Graphes, Théorie des Intégrales Feynman integrals Graph theory Graphentheorie (DE-588)4113782-6 gnd Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Feynman-integralen Grafen Graphes, Théorie des Intégrales Feynman integrals Graph theory Graphentheorie Pfadintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT nakanishinoboru graphtheoryandfeynmanintegrals |