Global World Functions

Franco Cardin; Antonio Marigonda

doi:10.7546/jgsp-2-2004-1-17

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Home > Journals > J. Geom. Symmetry Phys. > Volume 2 > Article

2004 Global World Functions

Franco Cardin, Antonio Marigonda

J. Geom. Symmetry Phys. 2: 1-17 (2004). DOI: 10.7546/jgsp-2-2004-1-17

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Abstract

Starting from the Amann-Conley-Zehnder finite reduction framework in the non-compact Viterbo's version we discuss the existence of global generating function with a finite number of auxiliary parameters describing the two-points Characteristic Relation related to the geodesic problem in the Hamiltonian formalism. 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.