  A nonlocal method of extracting the positive (or the negative) frequency part
of a field, based on knowledge of a 2-point function, leads to certain natural
generalizations of the normal ordering of quantum fields in classical
gravitational and electromagnetic backgrounds and illuminates the origin of the
recently discovered nonlocalities related to a local description of particles.
A local description of particle creation by gravitational backgrounds is given,
with emphasis on the case of black-hole evaporation. The formalism reveals a
previously hidden relation between various definitions of the particle current
and those of the energy-momentum tensor. The implications to particle creation
by classical backgrounds, as well as to the relation between vacuum energy,
dark matter, and cosmological constant, are discussed.
