  We discuss what is light-cone quantization on a curved spacetime also without
a null Killing vector. Then we consider as an example the light-cone
quantization of a scalar field on a background with a Killing vector and the
connection with the second quantization of the particle in the same background.
It turns out that the proper way to define the light-cone quantization is to
require that the constant light-cone time hypersurface is null or,
equivalently, that the particle Hamiltonian is free of square roots. Moreover,
in order to quantize the scalar theory it is necessary to use not the original
scalar rather a scalar field density, i.e. the Schr\"odinger wave functional
depends on a scalar density and not on the original field. Finally we recover
this result as the second quantization of a particle on the same background,
where it is necessary to add as input the fact that we are dealing with a
scalar density.
