Coherent State Operators in Loop Quantum Gravity

摘要

We present a new method for constructing operators in loop quantum gravity.The construction is an application of the general idea of "coherent statequantization", which allows one to associate a unique quantum operator to everyfunction on a classical phase space. Using the heat kernel coherent states ofHall and Thiemann, we show how to construct operators corresponding tofunctions depending on holonomies and fluxes associated to a fixed graph. Weconstruct the coherent state versions of the fundamental holonomy and fluxoperators, as well as the basic geometric operators of area, angle and volume.Our calculations show that the corresponding canonical operators are recoveredfrom the coherent state operators in the limit of large spins.