Heat kernels and Dirac operators:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2004]
|
| Schriftenreihe: | Grundlehren text editions
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originalausgabe erschien als Band 298 der Reihe Grundlehren der mathematischen Wissenschaften |
| Beschreibung: | IX, 363 Seiten |
| ISBN: | 3540200622 |
Internformat
MARC
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| 100 | 1 | |a Berline, Nicole |d 1944- |e Verfasser |0 (DE-588)113074964 |4 aut | |
| 245 | 1 | 0 | |a Heat kernels and Dirac operators |c Nicole Berline ; Ezra Getzler ; Michèle Vergne |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2004] | |
| 264 | 4 | |c © 2004 | |
| 300 | |a IX, 363 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Grundlehren text editions | |
| 500 | |a Originalausgabe erschien als Band 298 der Reihe Grundlehren der mathematischen Wissenschaften | ||
| 534 | |c 1992 | ||
| 650 | 4 | |a Differential forms | |
| 650 | 4 | |a Dirac equation | |
| 650 | 4 | |a Heat equation | |
| 650 | 4 | |a Index theorems | |
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| 650 | 0 | 7 | |a Wärmeleitungsgleichung |0 (DE-588)4188859-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kern |g Mathematik |0 (DE-588)4163599-1 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-010537610 | ||
Datensatz im Suchindex
| _version_ | 1804130290230099968 |
|---|---|
| adam_text | Contents
Introduction
..................................................... 1
1
Background
on
Differential
Geometry
........................... 13
1.1
Fibre Bundles and Connections
............................... 13
1.2
Riemannian Manifolds
...................................... 31
1.3
Superspaces
............................................... 37
1.4
Superconnections
.......................................... 41
1.5
Characteristic Classes
....................................... 44
1.6
The
Euler
and Thorn Classes
................................. 49
2
Asymptotic Expansion of the Heat Kernel
........................ 61
2.1
Differential Operators
....................................... 62
2.2
The Heat Kernel on Euclidean Space
.......................... 69
2.3
Heat Kernels
.............................................. 71
2.4
Construction of the Heat Kernel
.............................. 74
2.5
The Formal Solution
........................................ 79
2.6
The Trace of the Heat Kernel
................................. 85
2.7
Heat Kernels Depending on a Parameter
....................... 95
3
Clifford Modules and Dirac Operators
.......................... 99
3.1
The Clifford Algebra
........................................ 100
3.2
Spinors
................................................... 106
3.3
Dirac Operators
............................................ 110
3.4
Index of Dirac Operators
..................................... 118
3.5
The Lichnerowicz Formula
.................................. 122
3.6
Some Examples of Clifford Modules
.......................... 123
4
Index Density of Dirac Operators
...............................139
4.1
The Local Index Theorem
................................... 139
4.2
Mehler s Formula
.......................................... 149
4.3
Calculation of the Index Density
.............................. 153
VIII Contents
5
The Exponential Map and the Index Density
......................163
5.1
Jacobian of the Exponential Map on Principal Bundles
........... 164
5.2
The Heat Kernel of a Principal Bundle
......................... 168
5.3
Calculus with
Grassmann
and Clifford Variables
................ 173
5.4
The Index of Dirac Operators
................................ 177
6
The Equivariant Index Theorem
................................181
6.1
The Equivariant Index of Dirac Operators
...................... 182
6.2
The.Atiyah-Bott Fixed Point Formula
.......................... 183
6.3
Asymptotic Expansion of the Equivariant Heat Kernel
............ 187
6.4
The Local Equivariant Index Theorem
......................... 190
6.5
Geodesic Distance on a Principal Bundle
....................... 194
6.6
The heat kernel of an equivariant vector bundle
.................. 196
6.7
Proof of Proposition
6.13.................................... 199
7
Equivariant Differential Forms
.................................203
7.1
Equivariant Characteristic Classes
............................. 204
7.2
The Localization Formula
................................... 211
7.3
Bott s Formulas for Characteristic Numbers
.................... 219
7.4
Exact Stationary Phase Approximation
......................... 221
7.5
The Fourier Transform of Coadjoint Orbits
..................... 223
7.6
Equivariant Cohomology and Families
......................... 229
7.7
The
Bott
Class
............................................. 236
8
The Kirillov Formula for the Equivariant Index
...................243
8.1
The Kirillov Formula
....................................... 244
8.2
The Weyl and Kirillov Character Formulas
..................... 248
8.3
The Heat Kernel Proof of the Kirillov Formula
.................. 252
9
The Index Bundle
............................................ 263
9.1
The Index Bundle in Finite Dimensions
........................ 265
9.2
The Index Bundle of a Family of Dirac Operators
................ 273
9.3
The
Chem
Character of the Index Bundle
...................... 276
9.4
The Equivariant Index and the Index Bundle
.................... 287
9.5
The Case of Varying Dimension
.............................. 289
9.6
The Zeta-Function of a Laplacian
............................. 293
9.7
The Determinant Line Bundle
................................ 298
10
The Family Index Theorem
....................................311
10.1
Riemannian Fibre Bundles
................................... 314
10.2
Clifford Modules on Fibre Bundles
............................ 319
10.3
The Bismut Superconnection
................................. 326
10.4
The Family Index Density
................................... 330
10.5
The Transgression Formula
.................................. 338
10.6
The Curvature of the Determinant Line Bundle
.................. 341
10.7
The Kirillov Formula and Bismut s Index Theorem
.............. 344
Contents
IX
References
...................................................... 349
List of Notation
..................................................355
Index
........ ...................................................359
|
| any_adam_object | 1 |
| author | Berline, Nicole 1944- Getzler, Ezra 1962- Vergne, Michèle 1943- |
| author_GND | (DE-588)113074964 (DE-588)113074972 (DE-588)109340396 |
| author_facet | Berline, Nicole 1944- Getzler, Ezra 1962- Vergne, Michèle 1943- |
| author_role | aut aut aut |
| author_sort | Berline, Nicole 1944- |
| author_variant | n b nb e g eg m v mv |
| building | Verbundindex |
| bvnumber | BV017491705 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA377 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 SK 620 |
| ctrlnum | (OCoLC)53938889 (DE-599)BVBBV017491705 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017491705 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:18:41Z |
| institution | BVB |
| isbn | 3540200622 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010537610 |
| oclc_num | 53938889 |
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| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-384 DE-526 DE-83 DE-11 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-384 DE-526 DE-83 DE-11 DE-20 |
| physical | IX, 363 Seiten |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Grundlehren text editions |
| spelling | Berline, Nicole 1944- Verfasser (DE-588)113074964 aut Heat kernels and Dirac operators Nicole Berline ; Ezra Getzler ; Michèle Vergne Berlin ; Heidelberg Springer [2004] © 2004 IX, 363 Seiten txt rdacontent n rdamedia nc rdacarrier Grundlehren text editions Originalausgabe erschien als Band 298 der Reihe Grundlehren der mathematischen Wissenschaften 1992 Differential forms Dirac equation Heat equation Index theorems Indextheorem (DE-588)4140055-0 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Kern Mathematik (DE-588)4163599-1 gnd rswk-swf Kernfunktion (DE-588)4163607-7 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Differentialform (DE-588)4149772-7 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s DE-604 Dirac-Operator (DE-588)4150118-4 s Indextheorem (DE-588)4140055-0 s Wärmeleitungsgleichung (DE-588)4188859-5 s Kernfunktion (DE-588)4163607-7 s Differentialform (DE-588)4149772-7 s Kern Mathematik (DE-588)4163599-1 s Getzler, Ezra 1962- Verfasser (DE-588)113074972 aut Vergne, Michèle 1943- Verfasser (DE-588)109340396 aut Reproduktion von Berline, Nicole Heat kernels and Dirac operators Springer, 1992 3-540-53340-0 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berline, Nicole 1944- Getzler, Ezra 1962- Vergne, Michèle 1943- Heat kernels and Dirac operators Differential forms Dirac equation Heat equation Index theorems Indextheorem (DE-588)4140055-0 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Kern Mathematik (DE-588)4163599-1 gnd Kernfunktion (DE-588)4163607-7 gnd Dirac-Operator (DE-588)4150118-4 gnd Differentialoperator (DE-588)4012251-7 gnd Differentialform (DE-588)4149772-7 gnd |
| subject_GND | (DE-588)4140055-0 (DE-588)4188859-5 (DE-588)4163599-1 (DE-588)4163607-7 (DE-588)4150118-4 (DE-588)4012251-7 (DE-588)4149772-7 |
| title | Heat kernels and Dirac operators |
| title_auth | Heat kernels and Dirac operators |
| title_exact_search | Heat kernels and Dirac operators |
| title_full | Heat kernels and Dirac operators Nicole Berline ; Ezra Getzler ; Michèle Vergne |
| title_fullStr | Heat kernels and Dirac operators Nicole Berline ; Ezra Getzler ; Michèle Vergne |
| title_full_unstemmed | Heat kernels and Dirac operators Nicole Berline ; Ezra Getzler ; Michèle Vergne |
| title_short | Heat kernels and Dirac operators |
| title_sort | heat kernels and dirac operators |
| topic | Differential forms Dirac equation Heat equation Index theorems Indextheorem (DE-588)4140055-0 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Kern Mathematik (DE-588)4163599-1 gnd Kernfunktion (DE-588)4163607-7 gnd Dirac-Operator (DE-588)4150118-4 gnd Differentialoperator (DE-588)4012251-7 gnd Differentialform (DE-588)4149772-7 gnd |
| topic_facet | Differential forms Dirac equation Heat equation Index theorems Indextheorem Wärmeleitungsgleichung Kern Mathematik Kernfunktion Dirac-Operator Differentialoperator Differentialform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT berlinenicole heatkernelsanddiracoperators AT getzlerezra heatkernelsanddiracoperators AT vergnemichele heatkernelsanddiracoperators |