Light-cone quantization of scalar field on time-dependent backgrounds

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