Projective Limits of State Spaces I. Classical Formalism

Suzanne Lanéry (1) , Thomas Thiemann

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski (1977) and Andrzej Okołów (2009, 2013, 2014), which describes the states of a quantum (field) theory as projective families of density matrices. A short reading guide to the series can be found in  [27] . The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds  [27, subsection 2.1] . 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  [27, subsection 4.1] .

Mots clés: 18A30; 53D05; 81S10; 81T05; Field theory; Projective limits; Symplectic geometry; Algebras of observables; Constrained Hamiltonian systems; density matrix; symplectic; family; field theory: symplectic

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Suzanne Lanéry, Thomas Thiemann. Projective Limits of State Spaces I. Classical Formalism. J.Geom.Phys., 2017, 111, pp.6-39. ⟨10.1016/j.geomphys.2016.10.010⟩. ⟨hal-01553846⟩