A Nonlinear Model of a Quantum Minisuperspace System with Back Reaction

Abstract

We consider the quantum evolution of the space-independent mode of a $\lambda {\varphi }^4$ theory as a minisuperspace in the space of all $\varphi$. The motion of the wave packet in the minisuperspace is then compared to the motion of a wave packet in a larger minisuperspace consisting of the original minisuperspace plus one space-dependent mode. By comparing the motion of the two packets we develop criteria that tell us when the quantum evolution in the space-independent minisuperspace gives us useful information about the true evolution in the larger minisuperspace. These criteria serve as a toy model for similar(but much more complex) criteria that will tell us whether or when quantized gravitational minisuperspaces can possibly give any useful information about quantum gravity.

31 pages, 7 figures(available on request)