Projective Limits of State Spaces I. Classical Formalism

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 (field) theory as projective families of density matrices.

• The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds.
• In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them.