Quantum gravity, shadow states and quantum mechanics

By Abhay Ashtekar, Stephen Fairhurst, Josh Willis. 2002

297 citations recorded by the source corpus.

A programme was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. The model can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry. Maxwell fields will be discussed in the second paper of this series which further develops the programme.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2ac4e0b5a2fc19d6ce0c976d056896b61e921543

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

What is geometry in quantum theory (2004, background): “For instance, we are not concerned here with quantization of geometric objects such as loop quantum gravity [ 25-28 ], strings and branes”
Loop Quantum Cosmology (2005, background): “In fact, quantum mechanics is not very sensitive to the representation chosen [18] and one can use the most convenient one.”
Quantum geometry and the Schwarzschild singularity (2005, methodology): “From the structure of the algebra, it follows that the spectrum is naturally isomorphic to the Bohr compactification R̄(2)Bohr of the Abelian group R(2) [26, 27].”
Loop quantum gravity: an outside view (2005, background): “Showing that such a relation exists requires the field-theory analogues of the ‘shadow states’ for point particles [18].”