Quantization ambiguities in isotropic quantum geometry

By M. Bojowald. 2002

134 citations recorded by the source corpus.

Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown that these ambiguities do not affect the fate of the classical singularity, demonstrating that the absence of a singularity in loop quantum cosmology is a robust implication of the general quantization scheme. The calculations also allow conclusions about modified operators in the full theory. In particular, using holonomies in a non-fundamental representation of SU(2) to quantize connection components turns out to lead to significant corrections to classical behaviour at macroscopic volume for large values of the spin of the chosen representation.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8afb87c66eae9344f0fec81987175b5f7278bdb6

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In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Anomaly freedom in perturbative loop quantum gravity (2008, methodology): “It is possible to mimic the enhancement of inverse triad corrections even in exact homogeneous models by computing their correction function for operators based on higher representations of SU(2) instead of the fundamental one [57].”
Quantum Nature of the Big Bang: Improved dynamics (2006, background): “In this quantization, there are two ambiguities [5, 18], labelled by an half integer j and a real number l in the range 0 < l < 1.”
Mathematical structure of loop quantum cosmology (2003, background): “Furthermore, these features are robust [6,7].”
Loop Quantum Cosmology (2005, methodology): “Following the same procedure as above, we obtain eigenvalues [47, 50]”
Complexifier coherent states for quantum general relativity (2002, background): “However, graph dependent states, whether averaged or not, seem to be well suited for the semiclassical analysis of QGR with respect to coordinate independent operators.”
Introduction to Loop Quantum Cosmology (2011, background): “In fact, from the explicit calculations of inversevolume operators and their spectra in exactly isotropic models and for regular lattice states in the presence of inhomogeneities [41, 52, 66], correction functions implementing inverse-volume corrections approach the classical value always from above”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, background): “There are several choices involved in the construction, choosing a quantizable form for the inverse [57, 58] and a discretization of the derivative, but qualitative aspects to be discussed in what follows are not affected.”