In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been encountered in the earlier treatment. In this approach, gravity is formulated entirely in terms of Dirac observables without constraints, opening attractive new possibilities for quantization. In this paper we discuss the Poisson algebra of the resulting Dirac observables, associated with the intrinsic components of the Riemann tensor. This provides an explicit realization of the non-local algebra of observables for gravity that several authors have conjectured.
Gravitational Faraday rotation, gravitational spin Hall effect, and spin-refined causality analysis from Magnusian matrix in effective field theories of gravity
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of { \it (Bergmann) observable. This clarification leads to the proposal of a { \it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). b) The analysis of the so-called { \it Hole} phenomenology in strict connection with the Hamiltonian treatment of the initial val…
Hamiltonian Expression of Curvature Tensors in the York Canonical Basis: II) The Weyl Tensor, Weyl Scalars, the Weyl Eigenvalues and the Problem of the Observables of the Gravitational Field
Evidencing Quantum Gravity with Thermodynamical Observables
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）；Department of Physics, Royal Holloway, University of London（伦敦大学皇家霍洛威学院物理系）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院维也纳量子科学与技术中心）
