2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35613The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of quantum amplitudes for Euclidean Maxwell theory and linearized gravity. Within the framework of Faddeev-Popov formalism and zeta-function regularization, various choices of mixed boundary conditions lead to a deeper understanding of quantized gauge fields and quantum gravity in the presence of boundaries.14 pages, plain TEX, to appear in Proceedings of the Moscow Quantum Gravity Seminar, Moscow, June 12 - June 19, 1995General Relativity and Quantum Cosmologytext