New theory of radiative energy transfer in free electromagnetic fields

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Abstract
A new theory of radiative energy transfer in free, statistically stationary electromagnetic fields is presented. It provides a model for energy transport that is rigorous within the framework of the stochastic theory of the classical field as well as within the framework of the theory of the quantized field. Unlike the usual phenomenological model of radiative energy transfer that centers around a single scalar quantity (the specific intensity of radiation), our theory brings into evidence the need for characterizing the energy transport by means of two (related) quantities: a scalar and a vector that may be identified, in a well-defined sense, with "angular components" of the average electromagnetic energy density and of the average Poynting vector, respectively. Both of them are defined in terms of invariants of certain new electromagnetic correlation tensors. In the special case when the field is statistically homogeneous our model reduces to the usual one and our angular component of the average electromagnetic energy density, when multiplied by the vacuum speed of light, then acquires all the properties of the specific intensity of radiation. When the field is not statistically homogeneous our model reduces in good approximation to the usual phenomenological one, provided that the angular correlations between plane wave modes of the field extend over a sufficiently small solid angle of directions about the direction of propagation of each mode. It is tentatively suggested that, when suitably normalized, our angular component of the average electromagnetic energy density may be interpreted as a quasiprobability (general quantum-mechanical phase-space distribution function, such as Wigner's) for the position and the momentum of a photon.