Projective limits of state spaces I. Classical formalism

JOURNAL OF GEOMETRY AND PHYSICS

卷:111

Article

Lanery, Suzanne^1,2,3  Thiemann, Thomas¹ 

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

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

[3] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Campus Morelia,Apartado Postal 61-3 Xangari, Morelia 58089, Michoacan, Mexico

关键词: Field theory;    Projective limits;    Symplectic geometry;    Algebras of observables;    Constrained Hamiltonian systems;   

DOI  :  10.1016/j.geomphys.2016.10.010

来源: Elsevier

【 摘 要 】

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski (1977) and Andrzej Okolow (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]. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free