Projective Limits of State Spaces I. Classical Formalism
arXiv:1411.3589 · doi:10.1016/j.geomphys.2016.10.010
Abstract
In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okołów, 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.
51 pages, many figures
References in corpus (5)
- Algebraic Quantum Gravity (AQG) I. Conceptual Setup
- Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
- Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
- Projective Limits of State Spaces II. Quantum Formalism
- Projective Limits of State Spaces: Quantum Field Theory without a Vacuum
Cited by in corpus (14)
- Fusion basis for lattice gauge theory and loop quantum gravity
- Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
- Projective Limits of State Spaces II. Quantum Formalism
- Projective Loop Quantum Gravity I. State Space
- A modification of the projective construction of quantum states for field theories
- Hamiltonian Renormalisation V: Free Vector Bosons
- A new realization of quantum geometry
- Projective Limits of State Spaces: Quantum Field Theory without a Vacuum
- Projective Loop Quantum Gravity II. Searching for Semi-Classical States
- Quantum lattice gauge fields and groupoid C*-algebras
- Kinematic projective quantum states for Loop Quantum Gravity coupled to tensor fields
- Space of quantum states built over metrics of fixed signature
- Constrained projective quantum states for the degenerate Plebanski gravity
- Hilbert spaces built over metrics of fixed signature