An Introduction to Dirac Operators on Manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
2002
|
| Series: | Progress in Mathematical Physics
24 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory |
| Physical Description: | 1 Online-Ressource (XI, 211 p) |
| ISBN: | 9781461200659 9781461265962 |
| DOI: | 10.1007/978-1-4612-0065-9 |
Staff View
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461200659 9781461265962 |
| language | English |
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| spelling | Cnops, Jan Verfasser aut An Introduction to Dirac Operators on Manifolds by Jan Cnops Boston, MA Birkhäuser Boston 2002 1 Online-Ressource (XI, 211 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematical Physics 24 Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory Mathematics Group theory Operator theory Global differential geometry Group Theory and Generalizations Differential Geometry Operator Theory Theoretical, Mathematical and Computational Physics Mathematik Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 s Dirac-Operator (DE-588)4150118-4 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-0065-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cnops, Jan An Introduction to Dirac Operators on Manifolds Mathematics Group theory Operator theory Global differential geometry Group Theory and Generalizations Differential Geometry Operator Theory Theoretical, Mathematical and Computational Physics Mathematik Clifford-Algebra (DE-588)4199958-7 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| subject_GND | (DE-588)4199958-7 (DE-588)4150118-4 |
| title | An Introduction to Dirac Operators on Manifolds |
| title_auth | An Introduction to Dirac Operators on Manifolds |
| title_exact_search | An Introduction to Dirac Operators on Manifolds |
| title_full | An Introduction to Dirac Operators on Manifolds by Jan Cnops |
| title_fullStr | An Introduction to Dirac Operators on Manifolds by Jan Cnops |
| title_full_unstemmed | An Introduction to Dirac Operators on Manifolds by Jan Cnops |
| title_short | An Introduction to Dirac Operators on Manifolds |
| title_sort | an introduction to dirac operators on manifolds |
| topic | Mathematics Group theory Operator theory Global differential geometry Group Theory and Generalizations Differential Geometry Operator Theory Theoretical, Mathematical and Computational Physics Mathematik Clifford-Algebra (DE-588)4199958-7 gnd Dirac-Operator (DE-588)4150118-4 gnd |
| topic_facet | Mathematics Group theory Operator theory Global differential geometry Group Theory and Generalizations Differential Geometry Operator Theory Theoretical, Mathematical and Computational Physics Mathematik Clifford-Algebra Dirac-Operator |
| url | https://doi.org/10.1007/978-1-4612-0065-9 |
| work_keys_str_mv | AT cnopsjan anintroductiontodiracoperatorsonmanifolds |