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Projective Limits of State Spaces I. Classical Formalism

Abstract : 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] .
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Submitted on : Monday, July 3, 2017 - 5:28:33 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:11 PM

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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⟩

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