The Dirac spectrum:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in mathematics
1976 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 156 S. graph. Darst. |
| ISBN: | 9783642015694 9783642015700 |
Staff View
MARC
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| 100 | 1 | |a Ginoux, Nicolas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Dirac spectrum |c Nicolas Ginoux |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
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| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1976 | |
| 650 | 4 | |a Dirac, Équation de | |
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| 650 | 4 | |a Dirac equation | |
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Record in the Search Index
| _version_ | 1804139294321803264 |
|---|---|
| adam_text | Contents
1 Basics
of spin geometry
.............................................. 1
1.1
Spin group and spin structure
..................................... 1
1.2
Spinor bundle and Clifford multiplication
........................ 4
1.3
The Dirac operator
................................................. 9
1.4
Spinors on hypersurfaces and coverings
.......................... 19
1.5
Elliptic boundary conditions for the Dirac operator
............. 23
2
Explicit computations of spectra
.................................. 29
2.1
Spectrum of some non-negatively curved spaceforms
............ 29
2.2
Spectrum of some other homogeneous spaces
.................... 35
2.3
Small eigenvalues of some symmetric spaces
..................... 39
3
Lower eigenvalue estimates on closed manifolds
............... 41
3.1 Friedrich
s inequality
............................................... 41
3.2
Improving
Friedrich
s
inequality in presence
of a parallel form
................................................... 43
3.3
Improving Friedrich s inequality in
a conformai
way
............ 55
3.4
Improving Friedrich s inequality with the energy-
momentum tensor
.................................................. 58
3.5
Improving Friedrich s inequality with other curvature
components
......................................................... 60
3.6
Improving Friedrich s inequality on surfaces
of positive genus
.................................................... 61
3.7
Improving Friedrich s inequality on bounding manifolds
........ 64
4
Lower eigenvalue estimates
on compact manifolds with boundary
............................ 69
4.1
Case of the gAPS boundary condition
............................ 69
4.2
Case of the CHI boundary condition
............................. 70
4.3
Case of the MIT bag boundary condition
........................ 72
4.4
Case of the mgAPS boundary condition
.......................... 74
xii Contents
5
Upper eigenvalue bounds on closed manifolds
................. 77
5.1
Intrinsic upper bounds
............................................. 78
5.2
Extrinsic upper bounds
............................................ 85
6
Prescription of eigenvalues on closed manifolds
............... 93
6.1
Dirac isospectrality
................................................. 93
6.2
Harmonic spinors
................................................... 97
6.3
Prescribing the lower part of the spectrum
....................... 100
7
The Dirac spectrum on non-compact manifolds
...............103
7.1
Essential and point spectrum
...................................... 103
7.2
Explicit computations of spectra
..................................104
7.3
Lower bounds on the spectrum
....................................106
7.4
Absence of a spectral component
.................................109
8
Other topics related with the Dirac spectrum
.................113
8.1
Other eigenvalue estimates
........................................113
8.2
Spectral gap
........................................................116
8.3
Pinching Dirac eigenvalues
........................................ 117
8.4
Spectrum of other Dirac-type operators
..........................119
8.5
Conformai
spectral invariants
.....................................122
8.6
Convergence of eigenvalues
........................................125
8.7
Eta-invariants
.......................................................126
8.8
Positive mass theorems
............................................ 127
A The twistor and Killing spinor equations
........................131
A.I Definitions and examples
..........................................131
A.2 Elementary properties of twistor-spinors
......................... 134
A.3 Classification results for manifolds
with twistor-spinors
................................................ 140
A.4 Classification results for manifolds with Killing spinors
.........141
Bibliography
................................................................ 145
Index
......................................................................... 155
|
| any_adam_object | 1 |
| author | Ginoux, Nicolas |
| author_facet | Ginoux, Nicolas |
| author_role | aut |
| author_sort | Ginoux, Nicolas |
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| ctrlnum | (OCoLC)320495727 (DE-599)DNB993961924 |
| dewey-full | 530.143 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics 510 - Mathematics |
| dewey-raw | 530.143 510 |
| dewey-search | 530.143 510 |
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| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik |
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| indexdate | 2024-07-09T21:41:48Z |
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| isbn | 9783642015694 9783642015700 |
| language | English |
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| physical | XV, 156 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ginoux, Nicolas Verfasser aut The Dirac spectrum Nicolas Ginoux Berlin [u.a.] Springer 2009 XV, 156 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1976 Dirac, Équation de Dirac-Operator - Spektrum <Mathematik> Dirac equation Spin geometry Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 s Spektrum Mathematik (DE-588)4182180-4 s DE-604 Spektraltheorie (DE-588)4116561-5 s Lecture notes in mathematics 1976 (DE-604)BV000676446 1976 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017677861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ginoux, Nicolas The Dirac spectrum Lecture notes in mathematics Dirac, Équation de Dirac-Operator - Spektrum <Mathematik> Dirac equation Spin geometry Dirac-Operator (DE-588)4150118-4 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4182180-4 (DE-588)4116561-5 |
| title | The Dirac spectrum |
| title_auth | The Dirac spectrum |
| title_exact_search | The Dirac spectrum |
| title_full | The Dirac spectrum Nicolas Ginoux |
| title_fullStr | The Dirac spectrum Nicolas Ginoux |
| title_full_unstemmed | The Dirac spectrum Nicolas Ginoux |
| title_short | The Dirac spectrum |
| title_sort | the dirac spectrum |
| topic | Dirac, Équation de Dirac-Operator - Spektrum <Mathematik> Dirac equation Spin geometry Dirac-Operator (DE-588)4150118-4 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Dirac, Équation de Dirac-Operator - Spektrum <Mathematik> Dirac equation Spin geometry Dirac-Operator Spektrum Mathematik Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017677861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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