Aplicaciones de la variable compleja a la teoría cuántica de campos: regularización por funciones zeta y efecto Casimir

Abstract

The aim of this Degree Thesis is to prove the existence of an infinite vaccum energy due to quantum fluctuations and how to get a finite result while applying some boundary conditions. First of all, scalar field will be quantized in order to show it can be seen as a set of harmonic oscillators, which may all be in ground state, contribuying to a zero-point energy that diverges. In order to get a finite result by units of area, it will be used a classical and a zeta regularization for Dirichlet boundary conditions, the ones that Casimir originally used. That gives a discret spectrum that can be computed analitically. In the final part, a zeta regularization will be used for Robin boundary conditions, where it will be necessary to use numerical methods to get the spectrum.