2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91676We develop a spectral representation formalism to calculate the Casimir force in the non-retarded limit, between a spherical particle and a substrate, both with arbitrary local dielectric properties. This spectral formalism allows one to do a systematic study of the force as a function of the geometrical variables separately from the dielectric properties. We found that the force does not follow a simple power-law as a function of the separation between the sphere and substrate. As a consequence, the non-retarded Casimir force is enhanced by several orders of magnitude as the sphere approaches the substrate, while at large separations the dipolar term dominates the force.6 pages, contribution to the 6th Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT03), Norman, Oklahoma, September 15-19, 2003Quantum Physicstext