Prequantization of field theory (Q1387188)

The authors of the paper under review consider a local field theory specified by the Lagrangian density \({\mathcal L}\) defined on a curved spacetime \(Q.\) On the infinite-dimensional manifold of solutions of the corresponding field equation generated by the Cauchy data on a spacelike hypersurface \(\Sigma\subset Q\) one can introduce first vector fields, then the one-form \(\theta\) and finally the symplectic two-form \(\omega.\) These three objects are just the ingredients of the prequantization operator as given in the geometric quantization scheme. Applying this scheme to the Hamiltonian \(H\) canonically associated with \(\mathcal L\), the authors write down the abstract Schrödinger equation. No specific applications of the above procedure are presented.