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140122  eng 
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a 9789400964464

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1 

a Seifert, H.J.
e [editor]

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a Mathematical Aspects of Superspace
h Elektronische Ressource
c edited by H.J. Seifert, C.J.S. Clarke, A. Rosenblum

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3 
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a Proceedings of the NATO Advanced Research Workshop, Hamburg, Germany, July 1216, 1983

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a 1st ed. 1984

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a Dordrecht
b Springer Netherlands
c 1984, 1984

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a XII, 214 p
b online resource

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0 

a Nonlinear Realization of Supersymmetry  1. Introduction  2. The AkulovVolkov field  3. Superfields  4. Standard fields  5. N > 1/N = 1  6. N = 1 supergravity  References  Fields, Fibre Bundles and Gauge Groups  1. Manifolds  2. Fibre bundles  3. Gauge Groups  4. SpaceTime  Path Integration on Manifolds  1. Introduction  2. Gaussian measures, cylinder set measures, and the FeynmanKac formula  3. Feynman path integrals  4. Path integration on Riemannian manifolds  5. Gauge invariant equations; diffusion and differential forms  Acknowledgements, References  Graded Manifolds and Supermanifolds  Preface and cautionary note  0. Standard notation  1. The category GM  2. The geometric approach  3. Comparisons  4. Lie supergroups  Table: “All I know about supermanifolds”  References  Aspects of the Geometrical Approach to Supermanifolds  1. Abstract  2. Building superspace over an arbitrary spacetime  3. Super Lie groups  4. Compact supermanifolds with nonAbelian fundamental group  5. Developments and applications  References  Integration on Supermanifolds  1. Introduction  2. Standard integration theory  3. Integration over odd variables  4. Superforms  5. Integration on Er,s  6. Integration on supermanifolds  References  Remarks on Batchelor’s Theorem  Classical Supergravity  1. Definition of classical supergravity  2. Dynamical analysis of classical field theories  3. Formal dynamical analysis of classical supergravity  4. The exterior algebra formulation of classical supergravity  5. Does classical supergravity make sense?  Appendix: Notations and conventions  References  List of participants

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a Mathematical physics

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a Theoretical, Mathematical and Computational Physics

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1 

a Clarke, C.J.S.
e [editor]

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a Rosenblum, A.
e [editor]

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a SpringerLink (Online service)

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7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Nato Science Series C:, Mathematical and Physical Sciences

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u https://doi.org/10.1007/9789400964464?nosfx=y
x Verlag
3 Volltext

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a 530.1

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a Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe maticians and relativists who bring their experience in differen tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super symmetry is its relationship to the elementary particle spectrum
