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Solution to the difference equation of loop quantum cosmology for an anisotropic universe. The valley in the middle corresponds to the classical singularity which is penetrated by the quantum wave packet.

Since the discrete structure underlying quantum gravity leads to difference equations as the basic dynamical laws, new problems to determine properties of their solutions arise. The type of these equations is different from standard ones, and questions asked sometimes differ from what traditional investigations were interested in, which requires new tools to be developed. One issue is how to derive semiclassical properties of solutions in regimes where difference equations are close to continuum behavior. More generally, an important question is how such semiclassical behavior can emerge dynamically in a quantum system.

Publications

2001 · 2004 · 2005 · 2007 · All
M. Bojowald, G. Khanna and D. Cartin, "Lattice refining loop quantum cosmology, anisotropic models, and stability," Phys. Rev. D 76, 064018 (2007) Abstract/Comments
M. Bojowald and A. Rej, "Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology," Class. Quantum Gravity 22, 3399 – 3420 (2005) Abstract/Comments
M. Bojowald, D. Cartin and G. Khanna, "Generating function techniques for loop quantum cosmology," Class. Quantum Gravity 21, 4495 – 4509 (2004) Abstract/Comments
M. Bojowald and G. Date, "Consistency Conditions for Fundamentally Discrete Theories," Class. Quantum Gravity 21, 121 – 143 (2004) Abstract/Comments
M. Bojowald, "The Semiclassical Limit of Loop Quantum Cosmology," Class. Quantum Gravity 18, L109 – L116 (2001) Abstract/Comments

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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M. Bojowald : Difference equations