  In this paper we analyze how radiation effects influence the correlation
functions, the excess energy, and in turn the electron correlation energy of
the quantized electron gas at temperature $T=0$. To that aim we resort to a
statistical mechanical description of the quantum problem of electron
correlations, based on the path integral formalism. In previous works we
studied and found accurate results for the usual situation with the
electrostatic Coulomb interaction. Here the additional problem with radiation
is taken into account. This is facilitated by the equivalence to a dielectric
fluid for which correlation functions for dipolar moments are established. From
these functions follows the usual density-density (or charge-charge)
correlation function needed for the longitudinal electrostatic problem, and in
addition the one needed for the transverse radiation problem. While
electrostatic excess energy is negative, the transverse one is positive. This
quantity is small and decreases rapidly for decreasing densities. However, for
high densities it approaches the electrostatic contribution, eventually
becoming even larger. The part of the transverse energy from induced
correlations turns out to be very small. Also, the non-local longitudinal and
transverse dielectric constants of the electron gas are identified from the
induced correlation functions.
