ABSTRACT
In this chapter, the authors consider pure supergravity without couplings to matter fields. The problem of constructing the locally supersymmetric Lagrangian for the supergravity multiplet (the pure supergravity Lagrangian) can be tackled in two stages. First, construct the globally supersymmetric Lagrangian for the supergravity multiplet, and second use the Noether procedure to derive the locally supersymmetric Lagrangian from the globally super-symmetric Lagrangian. The authors show how the Noether procedure works for the simpler case of an ordinary global symmetry, before proceeding to the construction of the supergravity Lagrangian. The on-shell free Lagrangian for a chiral supermultiplet was just the sum of quadratic kinetic terms for the Weyl spinor field and the complex scalar field making up this supermultiplet.
