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The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformationsof the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.
This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.
The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformationsof the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.
This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.
Provides a detailed introduction to differential geometry on supermanifolds, including bundles, connections and integration
Focuses on super Riemann surfaces, supergeometric analogues of Riemann surfaces motivated by theoretical physics
Explains the relation between supergeometry and supersymmetry for the superconformal action on super Riemann surfaces
Introduction.- PART I Super Differential Geometry.- Linear Superalgebra.- Supermanifolds.- Vector Bundles.- Super Lie Groups.- Principal Fiber Bundles.- Complex Supermanifolds.- Integration.- PART II Super Riemann Surfaces.- Super Riemann Surfaces and Reductions of the Structure Group.- Connections on Super Riemann Surfaces.- Metrics and Gravitinos.- The Superconformal Action Functional.- Computations in Wess-Zumino Gauge.
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
xiii
305 S. 51 s/w Illustr. 305 p. 51 illus. |
| ISBN-13: | 9783030137571 |
| ISBN-10: | 3030137570 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-13757-1 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Keßler, Enno |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | Enno Keßler |
| Erscheinungsdatum: | 29.08.2019 |
| Gewicht: | 0,487 kg |
Provides a detailed introduction to differential geometry on supermanifolds, including bundles, connections and integration
Focuses on super Riemann surfaces, supergeometric analogues of Riemann surfaces motivated by theoretical physics
Explains the relation between supergeometry and supersymmetry for the superconformal action on super Riemann surfaces
Introduction.- PART I Super Differential Geometry.- Linear Superalgebra.- Supermanifolds.- Vector Bundles.- Super Lie Groups.- Principal Fiber Bundles.- Complex Supermanifolds.- Integration.- PART II Super Riemann Surfaces.- Super Riemann Surfaces and Reductions of the Structure Group.- Connections on Super Riemann Surfaces.- Metrics and Gravitinos.- The Superconformal Action Functional.- Computations in Wess-Zumino Gauge.
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
xiii
305 S. 51 s/w Illustr. 305 p. 51 illus. |
| ISBN-13: | 9783030137571 |
| ISBN-10: | 3030137570 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-13757-1 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Keßler, Enno |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | Enno Keßler |
| Erscheinungsdatum: | 29.08.2019 |
| Gewicht: | 0,487 kg |
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