Quantum gravity, shadow states, and quantum mechanics
  A program 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. Maxwell fields will be discussed in the second paper of this series which further develops the program and provides details. 
Abhay Ashtekar, Stephen Fairhurst, and Joshua L. Willis