On the number of soft quanta in classical field configurations

A crucial ingredient in the large-N quantum portrait of black holes proposed by Dvali and Gomez is the estimate of the number of soft quanta that make up the classical gravitational field. It is argued here that the coherent state formalism provides a way to calculate that number directly. As a consequence, the average energy of the soft quanta is such that the typical geometric size of the field source can be roughly interpreted as their de Broglie wavelength. The calculation is done for the electromagnetic field and for Newtonian gravity, and it is argued that the number of soft quanta should be unchanged in General Relativity due to the long range nature of gravity.

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