Brunnemann J, Thiemann T (2006)
Publication Status: Published
Publication Type: Journal article
Publication year: 2006
Publisher: IOP PUBLISHING LTD
Book Volume: 23
Pages Range: 1289-1346
Journal Issue: 4
DOI: 10.1088/0264-9381/23/4/014
The volume operator plays a crucial role in the definition of the quantum dynamics Of loop quantum gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the Volume spectrum. While closed formulae for the matrix elements are currently available in the literature, these are complicated polynomials in 6j symbols which ill turn are given in terms of Racah's formula which is too complicated in order to perform even numerical calculations for the semiclassically important regime of large spins. Hence, so far Hot even numerically the spectrum could be accessed. In this paper, we demonstrate that by means of the Elliot-Biedenharn identify one can get rid of all the 6j symbols for any valence of: the gauge-invariant vertex, thus immensely reducing the computational effort. We use the resulting compact formula to study numerically the spectrum of the gauge-invariant 4-vertex. The techniques derived in this paper-could also be of use for the analysis of spin-spin interaction Hamiltonians of many-particle problems in atomic and nuclear physics.
APA:
Brunnemann, J., & Thiemann, T. (2006). Simplification of the spectral analysis of the volume operator in loop quantum gravity. Classical and Quantum Gravity, 23(4), 1289-1346. https://dx.doi.org/10.1088/0264-9381/23/4/014
MLA:
Brunnemann, Johannes, and Thomas Thiemann. "Simplification of the spectral analysis of the volume operator in loop quantum gravity." Classical and Quantum Gravity 23.4 (2006): 1289-1346.
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