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Supergravity by Daniel Z. Freedman, Antoine Van Proeyen

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In this chapter we collect the ideas of differential geometry that are required to formulate general relativity and supergravity. There are several books, written for physicists, which explore this subject at greater length and greater depth [39, 40, 41, 42, 43, 44].

In general relativity spacetime is viewed as a differentiable manifold of dimension D ≥ 4 with a metric of Lorentzian signature (–, +, +, … , +) indicating one time dimension and D – 1 space dimensions. We assume that readers of this book are not intimidated by the idea of D – 4 hidden dimensions that are not directly observed. We will also consider manifolds of purely Euclidean ...

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