Projective Limits of State Spaces III. Toy-Models

Understand

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a quantum theory as projective families of density matrices.

• A strategy to implement the dynamics in this formalism was presented in our first paper, which we now test in two simple toy-models.
• The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level.
• In the second one, we reformulate the Schr\"odinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization.