Sistemas gaussianos não-autônomos: aplicação à cosmologia

Abstract

In this work a connection between dynamical quantum mechanical systems and scalar quantum field theory is built. Is verified that the Covariance Matrixs determinant is a time conserved quantity for Gaussian Systems under non autonomous Hamiltonians, and the generalizations for N and infinity dimensions is presented. Two cosmological models for the pre-heating period are treated, and a close connection between the Wigner function, squeezing and particle creation is found. A geometrical interpretation for the dynamics of the pre-heating is made possible, just as a experimental set up for testing cosmological hypothesis.