Global World Functions

Starting from the Amann-Conley-Zehnder finite reduction framework in the non-compact Viterbo’s version, we discuss the existence of global generat- ing function with a finite number of auxiliary parameters describing the two-points Characteristic Relation related to the geodesic problem in the Hamiltonian formal- ism. This applies both to Analytical Mechanics and to General Relativity - we construct a global object generalizing the World Function introduced by Synge, which is well-defined only locally. Whenever the auxiliary parameters can be fully removed, Synge’s World Function is restored.