  We explicitly express the Minkowski vacuum of a massless scalar field in
terms of the particle notion associated with suitable spherical conformal
killing fields. These fields are orthogonal to the light wavefronts originating
from a sphere with a radius of $r_{H}$ in flat spacetime: a bifurcate conformal
killing horizon that exhibits semiclassical features similar to those of black
hole horizons and Cauchy horizons of spherically symmetric black holes. Our
result highlights the quantum aspects of this analogy and extends the
well-known decomposition of the Minkowski vacuum in terms of Rindler modes,
which are associated with the boost Killing field normal to a pair of null
planes in Minkowski spacetime (the basis of the Unruh effect). While some
features of our result have been established by Kay and Wald's theorems in the
90s -- on quantum field theory in stationary spacetimes with bifurcate Killing
horizons -- the added value we provide here lies in the explicit expression of
the vacuum.
