Coherent states for canonical quantum general relativity and the infinite tensor product extension

By H. Sahlmann, T. Thiemann, O. Winkler. 2001

164 citations recorded by the source corpus.

Abstract We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b60a85d80f63e6689775ffa100a4f20203add6b9

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Citations in the corpus

Towards spinfoam cosmology (2010, background): “[13] Hanno Sahlmann, Thomas Thiemann, and Oliver Winkler.”
How far are we from the quantum theory of gravity (2003, background): “It is also understood how to construct coherent states which are peaked around classical configurations[130].”
Approaches To Quantum Gravity (2009, methodology): “Hence the states considered in Thiemann [2006a] are genuinely different from those in Thiemann and Winkler [2001a,b,c], Sahlmann et al. [2001]. This will turn out to be important. In fact, as will be discussed later, in order to be able to perform practical calculations for SU(2) with off diagonal e”
Quantization ambiguities in isotropic quantum geometry (2002, background): “(Another aspect which is not considered here is that semiclassical states should be used which are peaked in both the connection and the triad; see [23, 24, 25] for proposals.”
Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation (2002, methodology): “In [19], we chose Vol(supp(ω)) 3 and different observables, adapted to the graph in question, in order to have the lattice degrees of freedom well approximated and led to α ≈ 1/6.”
Loop Quantum Cosmology (2005, background): “, through a lattice as is indeed done in some coherent state constructions [184]).”
Quantum gravity, shadow states and quantum mechanics (2002, background): “They will now be discussed in detail and significantly extended in a series of papers, of which this is the first (see also [3, 4]).”
Gauge field theory coherent states (GCS): I. General properties (2000, background): “The main ideas and results of our proposal are summarized and reviewed in [48].”
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity (2007, unknown): “The aforementioned primary constraints are”
The Spin-Foam Approach to Quantum Gravity (2012, background): “1 Coherent states Coherent states associated with the representation theory of a compact group have been studied by Thiemann and collaborators [357, 355, 342, 360, 361, 362, 358, 50, 51, 177]; see also [76].”