Projective limits of state spaces III. Toy-models

JOURNAL OF GEOMETRY AND PHYSICS

卷:123

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;    Second quantization;    Fock representation;    Regularization;    Projective limits;    Algebras of observables;   

DOI  :  10.1016/j.geomphys.2017.08.007

来源: Elsevier

【 摘 要 】

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okolow (2009, 2014, 2013) [1,2], 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 Lanery (2016). A strategy to implement the dynamics in this formalism was presented in our first paper Lanery and Thiemann (2017) (see also Lanery, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrodinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization. (c) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free