Holdings: Introduction to symplectic Dirac operators

Introduction to symplectic Dirac operators:

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Bibliographic Details
Main Authors:	Habermann, Katharina 1966- (Author), Habermann, Lutz 1959- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2006
Series:	Lecture notes in mathematics 1887
Subjects:	Dirac-Operator - Symplektische Geometrie Dirac equation Dirac, Équation de Groupes symplectiques Géométrie symplectique Symplectic and contact topology Symplectic geometry Symplectic groups Topologie symplectique et de contact Symplektische Geometrie Dirac-Operator
Online Access:	Inhaltstext Inhaltsverzeichnis
Item Description:	Literaturverz. S. [115] - 118
Physical Description:	XII, 120 S. graph. Darst.
ISBN:	3540334203 9783540334200

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Record in the Search Index

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adam_text	CONTENTS 1 BACKGROUND ON SYMPLECTIC SPINORS . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 SYMPLECTIC GROUP AND CLIFFORD ALGEBRA . . . . . . . . . . . . . . . . . . . . . 1 1 .2 THE STONEVON NEUMANN THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 METAPLECTIC REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 SYMPLECTIC CLIFFORD MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 HERMITE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 SYMPLECTIC CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 SYMPLECTIC MANIFOLDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 CONSTRUCTIONS AND TORSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 SYMPLECTIC CURVATURE AND RICCI TENSORS . . . . . . . . . . . . . . . . . . . . 29 3 SYMPLECTIC SPINOR FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 METAPLECTIC STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 SYMPLECTIC SPINOR BUNDLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 SPLITTING OF THE SPINOR BUNDLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 SYMPLECTIC DIRAC OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1DEFINITION OF THE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 DEPENDENCE ON THE SYMPLECTIC CONNECTION . . . . . . . . . . . . . . . . . . 52 4.3 DEPENDENCE ON THE METAPLECTIC STRUCTURE . . . . . . . . . . . . . . . . . . . 57 4.4 DEPENDENCE ON THE ALMOST COMPLEX STRUCTURE . . . . . . . . . . . . . . 62 4.5 FORMAL SELF-ADJOINTNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 XII CONTENTS 5 AN ASSOCIATED SECOND ORDER OPERATOR . . . . . . . . . . . . . . . . . . . . 67 5.1DEFINITION AND ELLIPTICITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 A WEITZENB¨ OCK FORMULA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.3 SPLITTING OF THE OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6THE K¨ AHLER CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.1THE OPERATOR P ON K¨ AHLER MANIFOLDS . . . . . . . . . . . . . . . . . . . . . . 81 6.2 LOWER BOUND ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.3 THE SPECTRUM OF P ON C P 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7 FOURIER TRANSFORM FOR SYMPLECTIC SPINORS . . . . . . . . . . . . . . . . . . 97 7.1DEFINITION OF THE TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.2 BASIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.3 SYMMETRY OF THE SPECTRA OF D AND D . . . . . . . . . . . . . . . . . . . . . . 99 8 LIE DERIVATIVE AND QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 01 8.1LIE DERIVATIVE OF SYMPLECTIC SPINOR FIELDS . . . . . . . . . . . . . . . . . . 101 8.2 SCHR¨ ODINGER EQUATION FOR QUADRATIC HAMILTONIANS . . . . . . . . . . . 109 8.3 LIE DERIVATIVE AS QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 5 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 9
adam_txt	CONTENTS 1 BACKGROUND ON SYMPLECTIC SPINORS . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 SYMPLECTIC GROUP AND CLIFFORD ALGEBRA . . . . . . . . . . . . . . . . . . . . . 1 1 .2 THE STONEVON NEUMANN THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 METAPLECTIC REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 SYMPLECTIC CLIFFORD MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 HERMITE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 SYMPLECTIC CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 SYMPLECTIC MANIFOLDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 CONSTRUCTIONS AND TORSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 SYMPLECTIC CURVATURE AND RICCI TENSORS . . . . . . . . . . . . . . . . . . . . 29 3 SYMPLECTIC SPINOR FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 METAPLECTIC STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 SYMPLECTIC SPINOR BUNDLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 SPLITTING OF THE SPINOR BUNDLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 SYMPLECTIC DIRAC OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1DEFINITION OF THE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 DEPENDENCE ON THE SYMPLECTIC CONNECTION . . . . . . . . . . . . . . . . . . 52 4.3 DEPENDENCE ON THE METAPLECTIC STRUCTURE . . . . . . . . . . . . . . . . . . . 57 4.4 DEPENDENCE ON THE ALMOST COMPLEX STRUCTURE . . . . . . . . . . . . . . 62 4.5 FORMAL SELF-ADJOINTNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 XII CONTENTS 5 AN ASSOCIATED SECOND ORDER OPERATOR . . . . . . . . . . . . . . . . . . . . 67 5.1DEFINITION AND ELLIPTICITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 A WEITZENB¨ OCK FORMULA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.3 SPLITTING OF THE OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6THE K¨ AHLER CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.1THE OPERATOR P ON K¨ AHLER MANIFOLDS . . . . . . . . . . . . . . . . . . . . . . 81 6.2 LOWER BOUND ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.3 THE SPECTRUM OF P ON C P 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7 FOURIER TRANSFORM FOR SYMPLECTIC SPINORS . . . . . . . . . . . . . . . . . . 97 7.1DEFINITION OF THE TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.2 BASIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.3 SYMMETRY OF THE SPECTRA OF D AND D . . . . . . . . . . . . . . . . . . . . . . 99 8 LIE DERIVATIVE AND QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 01 8.1LIE DERIVATIVE OF SYMPLECTIC SPINOR FIELDS . . . . . . . . . . . . . . . . . . 101 8.2 SCHR¨ ODINGER EQUATION FOR QUADRATIC HAMILTONIANS . . . . . . . . . . . 109 8.3 LIE DERIVATIVE AS QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 5 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 9
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series	Lecture notes in mathematics
series2	Lecture notes in mathematics
spelling	Habermann, Katharina 1966- Verfasser (DE-588)112163912 aut Introduction to symplectic Dirac operators K. Habermann ; L. Habermann Berlin [u.a.] Springer 2006 XII, 120 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1887 Literaturverz. S. [115] - 118 Dirac-Operator - Symplektische Geometrie Dirac equation Dirac, Équation de Groupes symplectiques Géométrie symplectique Symplectic and contact topology Symplectic geometry Symplectic groups Topologie symplectique et de contact Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 s Symplektische Geometrie (DE-588)4194232-2 s DE-604 Habermann, Lutz 1959- Verfasser (DE-588)121640450 aut Lecture notes in mathematics 1887 (DE-604)BV000676446 1887 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2786238&prov=M&dok_var=1&dok_ext=htm Inhaltstext SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014929268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Habermann, Katharina 1966- Habermann, Lutz 1959- Introduction to symplectic Dirac operators Lecture notes in mathematics Dirac-Operator - Symplektische Geometrie Dirac equation Dirac, Équation de Groupes symplectiques Géométrie symplectique Symplectic and contact topology Symplectic geometry Symplectic groups Topologie symplectique et de contact Symplektische Geometrie (DE-588)4194232-2 gnd Dirac-Operator (DE-588)4150118-4 gnd
subject_GND	(DE-588)4194232-2 (DE-588)4150118-4
title	Introduction to symplectic Dirac operators
title_auth	Introduction to symplectic Dirac operators
title_exact_search	Introduction to symplectic Dirac operators
title_exact_search_txtP	Introduction to symplectic Dirac operators
title_full	Introduction to symplectic Dirac operators K. Habermann ; L. Habermann
title_fullStr	Introduction to symplectic Dirac operators K. Habermann ; L. Habermann
title_full_unstemmed	Introduction to symplectic Dirac operators K. Habermann ; L. Habermann
title_short	Introduction to symplectic Dirac operators
title_sort	introduction to symplectic dirac operators
topic	Dirac-Operator - Symplektische Geometrie Dirac equation Dirac, Équation de Groupes symplectiques Géométrie symplectique Symplectic and contact topology Symplectic geometry Symplectic groups Topologie symplectique et de contact Symplektische Geometrie (DE-588)4194232-2 gnd Dirac-Operator (DE-588)4150118-4 gnd
topic_facet	Dirac-Operator - Symplektische Geometrie Dirac equation Dirac, Équation de Groupes symplectiques Géométrie symplectique Symplectic and contact topology Symplectic geometry Symplectic groups Topologie symplectique et de contact Symplektische Geometrie Dirac-Operator
url	http://deposit.dnb.de/cgi-bin/dokserv?id=2786238&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014929268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT habermannkatharina introductiontosymplecticdiracoperators AT habermannlutz introductiontosymplecticdiracoperators

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