2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116297By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this kinetic term's metric. This new geometrical standpoint sheds light on some foundational issues of QFT and brings to the forefront core aspects of field theory.14 pages, 18 figures; fonts corrected, for a higher definition version, check http://chep.het.brown.edu/High Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - PhenomenologyMathematical PhysicsDifferential Geometrytext