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.
Global world functions
MARIGONDA, Antonio
2004-01-01
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.
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