EMERGENCE OF THE SIMULTANEOUS CONTINUOUS AND DISCRETE STRUCTURE OF THE ELECTROMAGNETIC FIELD

Abstract

We analyze a quantum central limit theorem without centering and a quantum Poisson limit theorem on an array of indistinguishable quanta and investigate the emergence of the continuous and discrete structure of the quantized electromagnetic field in classical states. Moreover, we identify the observables that converge to the random variables which induce the mixing measure of a classical state. Finally, we show that the transformation to normal order is a conditional expectation replacing expectations of functions of the annihilation and creation operator by expectations with respect to global classical observables of the array.