  A new approach to the concept of particles and their production in quantum
field theory is developed. A local operator describing the current of particle
density is constructed for scalar and spinor fields in arbitrary gravitational
and electromagnetic backgrounds. This enables one to describe particles in a
local, general-covariant and gauge-invariant way. However, the current depends
on the choice of a 2-point function. There is a choice that leads to the local
non-conservation of the current in a gravitational or an electromagnetic
background, which describes local particle production consistent with the usual
global description based on the Bogoliubov transformation. The most natural
choice based on the Green function calculated using the Schwinger-DeWitt method
leads to the local conservation of the current, provided that interactions with
quantum fields are absent. Interactions with quantum fields lead to the local
non-conservation of the current which describes local particle production
consistent with the usual global description based on the interaction picture.
