Gauge field theory coherent states (GCS): III. Ehrenfest theorems

By T. Thiemann, O. Winkler. 2000

156 citations recorded by the source corpus.

In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and were later generalized to gauge field theory by Ashtekar, Lewandowski, Marolf, Mourao and Thiemann. In this paper we establish the `Ehrenfest property' of these states which are labelled by a point (A,E), a connection and an electric field, in the classical phase space. By this we mean that the expectation values of the elementary operators (and of their commutators divided by i, respectively) in a coherent state labelled by the (A,E) are, to zeroth order in , given by the values of the corresponding elementary functions (and of their Poisson brackets, respectively) at the point (A,E). These results can be extended to all polynomials of elementary operators and to a certain non-polynomial function of the elementary operators associated with the volume operator of quantum general relativity. These findings are another step towards establishing that the infinitesimal quantum dynamics of quantum general relativity might, to lowest order in , indeed be given by classical general relativity.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fd4697202b4901a9751c56af30fbc550b210c72d

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Citations in the corpus

Towards spinfoam cosmology (2010, unknown): “[11] Thomas Thiemann and Oliver Winkler.”
The Spin-Foam Approach to Quantum Gravity (2012, background): “1 Coherent states Coherent states associated to the representation theory of a compact group have been studied by Thiemann and collaborators [351, 349, 335, 349, 354, 355, 356, 352, 46, 47, 171] see also [70].”
Gauge field theory coherent states (GCS): II. Peakedness properties (2000, background): “Also, in this section we will take all quantities to be dimensionless for simplicity, the incoporation of dimensionful parameters will be discussed in the next section.”
Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation (2002, methodology): “Thus, due to the Ehrenfest properties proved in [11] we conclude that at least for coherent states based on graphs with cubic topologies the operators (3.”
Gauge field theory coherent states (GCS): I. General properties (2000, background): “In the third paper [44] of this series we prove Ehrenfest theorems for our coherent states.”