Projective limits of state spaces II. Quantum formalism

JOURNAL OF GEOMETRY AND PHYSICS

卷:116

Article

Lanery, Suzanne^1,2  Thiemann, Thomas¹ 

[1] Friedrich Alexander Univ Erlangen Nurnberg, Inst Quantum Grav, Staudtstr 7-B2, D-91058 Erlangen, Germany

[2] Univ Francois Rabelais Tours, Lab Math & Phys Theor, UFR Sci & Tech, Parc Grandmont, F-37200 Tours, France

关键词: Quantum field theory;    Projective limits;    Algebras of observables;    Geometric quantization;    Position representation;    Holomorphic quantization;   

DOI  :  10.1016/j.geomphys.2017.01.011

来源: Elsevier

【 摘 要 】

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okolow (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanky (2016). After discussing the formalism at the classical level in a first paper (Lanery, 2017), 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 (Lanery, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okolow (2013), 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 (Lanky, 2016, subsection 2.2) [1]. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free