  We study quantization of a self-interacting scalar field within the unfolded
dynamics approach. To this end we find and analyze a classical unfolded system
describing 4d off-shell scalar field with a general self-interaction potential.
Then we systematically construct three different but related unfolded
formulations of the corresponding quantum field theory, supporting them with
illustrative calculations: an unfolded functional Schwinger-Dyson system, an
unfolded system for correlation functions and an unfolded effective system for
vertex functions. The most curious feature we reveal is that an unfolded
quantum commutator gets naturally regularized: a standard delta-function is
replaced with a heat kernel, parameterized by the unfolded proper time. We also
identify an auxiliary 5d system, having this proper time as a physical time,
which generates 4d scalar action as its on-shell action.
