Heat kernels and Dirac operators:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Edition: | Corr. 2. print. |
| Series: | Grundlehren der mathematischen Wissenschaften
298 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 356 - 360 |
| Physical Description: | VII, 368 S. |
| ISBN: | 3540533400 0387533400 |
Staff View
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 |
| 250 | |a Corr. 2. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a VII, 368 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 298 | |
| 500 | |a Literaturverz. S. 356 - 360 | ||
| 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 Kernfunktion |0 (DE-588)4163607-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wärmeleitungsgleichung |0 (DE-588)4188859-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1807502170870775808 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
ACKNOWLEDGEMENTS
.
13
CHAPTER
1.
BACKGROUND
ON
DIFFERENTIAL
GEOMETRY
14
1.1.
FIBRE
BUNDLES
AND
CONNECTIONS
.
14
1.2.
RIEMANNIAN
MANIFOLDS
.
32
1.3.
SUPERSPACES
.
38
1.4.
SUPERCONNECTIONS
.
43
1.5.
CHARACTERISTIC
CLASSES
.
46
1.6.
THE
EULER
AND
THOM
CLASSES
.
51
BIBLIOGRAPHIC
NOTES
.
61
CHAPTER
2.
ASYMPTOTIC
EXPANSION
OF
THE
HEAT
KERNEL
63
2.1.
DIFFERENTIAL
OPERATORS
.
64
2.2.
THE
HEAT
KERNEL
ON
EUCLIDEAN
SPACE
.
72
2.3.
HEAT
KERNELS
.
74
2.4.
CONSTRUCTION
OF
THE
HEAT
KERNEL
.
77
2.5.
THE
FORMAL
SOLUTION
.
81
2.6.
THE
TRACE
OF
THE
HEAT
KERNEL
.
87
2.7.
HEAT
KERNELS
DEPENDING
ON
A
PARAMETER
.
98
BIBLIOGRAPHIC
NOTES
.
101
CHAPTER
3.
CLIFFORD
MODULES
AND
DIRAC
OPERATORS
102
3.1.
THE
CLIFFORD
ALGEBRA
.
103
3.2.
SPINORS
.
109
3.3.
DIRAC
OPERATORS
.
113
3.4.
INDEX
OF
DIRAC
OPERATORS
.
122
3.5.
THE
LICHNEROWICZ
FORMULA
.
126
3.6.
SOME
EXAMPLES
OF
CLIFFORD
MODULES
.
127
THE
DERHAM
OPERATOR
.
128
THE
SIGNATURE
OPERATOR
.
131
THE
DIRAC
OPERATOR
ON
A
SPIN-MANIFOLD
.
134
THE
D-OPERATOR
ON
A
KAHLER
MANIFOLD
.
135
BIBLIOGRAPHIC
NOTES
.
141
VI
CONTENTS
CHAPTER
4.
INDEX
DENSITY
OF
DIRAC
OPERATORS
143
4.1.
THE
LOCAL
INDEX
THEOREM
.
143
THE
GAUSS-BONNET-CHERN
THEOREM
.
148
THE
HIRZEBRUCH
SIGNATURE
THEOREM
.
150
THE
INDEX
THEOREM
FOR
THE
DIRAC
OPERATOR
.
151
THE
RIEMANN-ROCH-HIRZEBRUCH
THEOREM
.
151
4.2.
MEHLER
'
S
FORMULA
.
153
4.3.
CALCULATION
OF
THE
INDEX
DENSITY
.
157
BIBLIOGRAPHIC
NOTES
.
164
ADDITIONAL
REMARKS
.
166
CHAPTER
5.
THE
EXPONENTIAL
MAP
AND
THE
INDEX
DENSITY
167
5.1.
JACOBIAN
OF
THE
EXPONENTIAL
MAP
ON
PRINCIPAL
BUNDLES
.
168
5.2.
THE
HEAT
KERNEL
OF
A
PRINCIPAL
BUNDLE
.
172
5.3.
CALCULUS
WITH
GRASSMANN
AND
CLIFFORD
VARIABLES
.
178
5.4.
THE
INDEX
OF
DIRAC
OPERATORS
.
181
BIBLIOGRAPHIC
NOTES
.
183
CHAPTER
6.
THE
EQUIVARIANT
INDEX
THEOREM
184
6.1.
THE
EQUIVARIANT
INDEX
OF
DIRAC
OPERATORS
.
185
6.2.
THE
ATIYAH-BOTT
FIXED
POINT
FORMULA
.
186
6.3.
ASYMPTOTIC
EXPANSION
OF
THE
EQUIVARIANT
HEAT
KERNEL
.
190
6.4.
THE
LOCAL
EQUIVARIANT
INDEX
THEOREM
.
193
6.5.
GEODESIC
DISTANCE
ON
A
PRINCIPAL
BUNDLE
.
197
6.6.
THE
HEAT
KERNEL
OF
AN
EQUIVARIANT
VECTOR
BUNDLE
.
199
6.7.
PROOF
OF
PROPOSITION
6.13
.
202
BIBLIOGRAPHIC
NOTES
.
204
CHAPTER
7.
EQUIVARIANT
DIFFERENTIAL
FORMS
205
7.1.
EQUIVARIANT
CHARACTERISTIC
CLASSES
.
206
7.2.
THE
LOCALIZATION
FORMULA
.
213
7.3.
BOTT
'
S
FORMULAS
FOR
CHARACTERISTIC
NUMBERS
.
.
221
7.4.
EXACT
STATIONARY
PHASE
APPROXIMATION
.
224
7.5.
THE
FOURIER
TRANSFORM
OF
COADJOINT
ORBITS
.
226
7.6.
EQUIVARIANT
COHOMOLOGY
AND
FAMILIES
.
232
7.7.
THE
BOTT
CLASS
.
239
BIBLIOGRAPHIC
NOTES
.
244
ADDITIONAL
REMARKS
.
245
CHAPTER
8.
THE
KIRILLOV
FORMULA
FOR
THE
EQUIVARIANT
INDEX
246
8.1.
THE
KIRILLOV
FORMULA
.
247
8.2.
THE
WEYL
AND
KIRILLOV
CHARACTER
FORMULAS
.
251
8.3.
THE
HEAT
KERNEL
PROOF
OF
THE
KIRILLOV
FORMULA
.
256
BIBLIOGRAPHIC
NOTES
.
265
ADDITIONAL
REMARKS
.
266
CONTENTS
VII
CHAPTER
9.
THE
INDEX
BUNDLE
267
9.1.
THE
INDEX
BUNDLE
IN
FINITE
DIMENSIONS
.
269
9.2.
THE
INDEX
BUNDLE
OF
A
FAMILY
OF
DIRAC
OPERATORS
.
277
9.3.
THE
CHERN
CHARACTER
OF
THE
INDEX
BUNDLE
.
281
9.4.
THE
EQUIVARIANT
INDEX
AND
THE
INDEX
BUNDLE
.
292
9.5.
THE
CASE
OF
VARYING
DIMENSION
.
294
9.6.
THE
ZETA-FUNCTION
OF
A
LAPLACIAN
.
299
9.7.
THE
DETERMINANT
LINE
BUNDLE
.
304
APPENDIX.
MORE
ON
HEAT
KERNELS
.
309
BIBLIOGRAPHIC
NOTES
.
315
CHAPTER
10.
THE
FAMILY
INDEX
THEOREM
316
10.1.
RIEMANNIAN
FIBRE
BUNDLES
.
319
10.2.
CLIFFORD
MODULES
ON
FIBRE
BUNDLES
.
324
10.3.
THE
BISMUT
SUPERCONNECTION
.
331
10.4.
THE
FAMILY
INDEX
DENSITY
.
335
10.5.
THE
TRANSGRESSION
FORMULA
.
343
10.6.
THE
CURVATURE
OF
THE
DETERMINANT
LINE
BUNDLE
.
347
10.7.
THE
KIRILLOV
FORMULA
AND
BISMUT
'
S
INDEX
THEOREM
.
350
BIBLIOGRAPHIC
NOTES
.
354
BIBLIOGRAPHY
355
LIST
OF
NOTATIONS
360
INDEX
364 |
| 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- |
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| ctrlnum | (OCoLC)33948563 (DE-599)BVBBV010494101 |
| 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 |
| edition | Corr. 2. print. |
| format | Book |
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| id | DE-604.BV010494101 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T00:33:15Z |
| institution | BVB |
| isbn | 3540533400 0387533400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006992844 |
| oclc_num | 33948563 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-384 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-384 DE-11 |
| physical | VII, 368 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Berline, Nicole 1944- Verfasser (DE-588)113074964 aut Heat kernels and Dirac operators Nicole Berline ; Ezra Getzler ; Michèle Vergne Corr. 2. print. Berlin [u.a.] Springer 1996 VII, 368 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 298 Literaturverz. S. 356 - 360 Differential forms Dirac equation Heat equation Index theorems Kern Mathematik (DE-588)4163599-1 gnd rswk-swf Differentialform (DE-588)4149772-7 gnd rswk-swf Kernfunktion (DE-588)4163607-7 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Indextheorem (DE-588)4140055-0 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 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 1\p DE-604 Kern Mathematik (DE-588)4163599-1 s 2\p DE-604 Getzler, Ezra 1962- Verfasser (DE-588)113074972 aut Vergne, Michèle 1943- Verfasser (DE-588)109340396 aut Grundlehren der mathematischen Wissenschaften 298 (DE-604)BV000000395 298 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006992844&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berline, Nicole 1944- Getzler, Ezra 1962- Vergne, Michèle 1943- Heat kernels and Dirac operators Grundlehren der mathematischen Wissenschaften Differential forms Dirac equation Heat equation Index theorems Kern Mathematik (DE-588)4163599-1 gnd Differentialform (DE-588)4149772-7 gnd Kernfunktion (DE-588)4163607-7 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Differentialoperator (DE-588)4012251-7 gnd Indextheorem (DE-588)4140055-0 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| subject_GND | (DE-588)4163599-1 (DE-588)4149772-7 (DE-588)4163607-7 (DE-588)4188859-5 (DE-588)4012251-7 (DE-588)4140055-0 (DE-588)4150118-4 |
| 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 Kern Mathematik (DE-588)4163599-1 gnd Differentialform (DE-588)4149772-7 gnd Kernfunktion (DE-588)4163607-7 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Differentialoperator (DE-588)4012251-7 gnd Indextheorem (DE-588)4140055-0 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| topic_facet | Differential forms Dirac equation Heat equation Index theorems Kern Mathematik Differentialform Kernfunktion Wärmeleitungsgleichung Differentialoperator Indextheorem Dirac-Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006992844&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT berlinenicole heatkernelsanddiracoperators AT getzlerezra heatkernelsanddiracoperators AT vergnemichele heatkernelsanddiracoperators |