Projective Limits of State Spaces II. Quantum Formalism
arXiv:1411.3590 · doi:10.1016/j.geomphys.2017.01.011
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 theory as projective families of density matrices. After discussing the formalism at the classical level in a first paper, the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów [Okołów 2013, arXiv:1304.6330], that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces.
56 pages, 2 figures
References in corpus (7)
- Quantum fields in curved spacetime
- Flux formulation of loop quantum gravity: Classical framework
- Projective Limits of State Spaces I. Classical Formalism
- Projective Loop Quantum Gravity I. State Space
- Projective Limits of State Spaces: Quantum Field Theory without a Vacuum
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Cited by in corpus (14)
- Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
- Projective Limits of State Spaces I. Classical 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
- Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
- 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