  In this work, starting from commutation relations between phase-space
operators (in "first quantization") we define averaged creation and
annihilation operators and show that they satisfy a simple, deformed
commutation relation. By extending this relation to the quantized
electromagnetic field, we determine the new vacuum state which has a non-zero
component in standard occupied states. In addition we are led to non-linear de
Broglie relations for photons, which appreciably depart from linearity only in
the very-high-energy regime. The nonlinear Compton scattering that follows from
these assumptions is discussed. We suggest that this hypothesis may be a way to
deal with the transparency of the electromagnetic background light (EBL) and
show that it may lead to an attenuation in the cosmological-constant problem of
several orders of magnitude.
