2000/01/31 by Madhavan Varadarajan, José A. Zapata
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical limit #Classical mechanics #Cosmology and Gravitation Theories #Countable set #Diffeomorphism #General covariance #General relativity #Hamiltonian (control theory) #Kinematics #Limit (mathematics) #Loop quantum gravity #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #gr-qc #hep-lat #hep-th
paper · pdf · doi:10.1088/0264-9381/17/19/309
published as Class.Quant.Grav.17:4085-4110,2000 · Replaced with substantially revised version
arxiv created 2000/08/09 · openalex publication_date 2000/09/19 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyse the classical limit of kinematic loop quantum gravity in which the diffeomorphism and Hamiltonian constraints are ignored. We show that there are no quantum states in which the primary variables of the loop approach, namely the SU (2) holonomies along all possible loops, approximate their classical counterparts. At most a countable number of loops must be specified. To preserve spatial covariance, we choose this set of loops to be based on physical lattices specified by the quasiclassical states themselves. We construct `macroscopic' operators based on such lattices and propose that these operators be used to analyse the classical limit. Thus, our aim is to approximate classical data using states in which appropriate macroscopic operators have low quantum fluctuations. Although, in principle, the holonomies of `large' loops on these lattices could be used to analyse the classical limit, we argue that it may be simpler to base the analysis on an alternate set of `flux'-based operators. We explicitly construct candidate quasiclassical states in two spatial dimensions and indicate how these constructions may generalize to three dimensions. We discuss the less robust aspects of our proposal with a view towards possible modifications. Finally, we show that our proposal also applies to the diffeomorphism-invariant Rovelli model which couples a matter reference system to the Hussain-Kuchar model.