Seminario Mundo/Lógica/Modelos: 24 de abril. Åsa Hirvonen (U-Helsinki) - Ultraproduct approaches to finite dimensional approximations - eigenvectors and distributions
Andrés Villaveces
Abstract: There is a tradition in physics of approximating quantum mechanical systems by finite-dimensional spaces and using them for calculations. Together with Tapani Hyttinen we have studied ultraproduct approaches to motivating such approximations. The first approach builds eigenvectors in an ultraproduct model. There one can calculate the Feynman propagator (used to describe time evolution of the system), but not as directly as one would suspect, but using an averaging trick. The second approach looks at distributions instead of eigenvectors in an ultraproduct model. Again, finite-dimensional approximations can be used to calculate
propagators (in a rather restricted setting), but the same need for averaging turns up.
In the talk I will present both ultraproduct constructions, and explain why the generalized eigenvectors these present cannot directly be used to calculate propagators in a physics course book style.
Andrés Villaveces
Andrés Villaveces
avillavecesn.net
Departamento de Matemáticas - Edificio 404
Universidad Nacional de Colombia
AK 30 # 45-03
111321 - Bogotá - Colombia
Tel: +57 601 3165000 ext 13209