  Expressing currents and their fluctuations at the terminals of a multi-probe
conductor in terms of the wave functions of carriers injected into the Fermi
sea provides new insight into the physics of electric currents. This approach
helps us to identify two physically different contributions to shot noise. In
the quantum coherent regime, when current is carried by non-overlapping
wave-packets, the product of current fluctuations in different leads, the
cross-correlation noise, is determined solely by the duration of the wave
packet. In contrast, the square of the current fluctuations in one lead, the
auto-correlation noise, is additionally determined by the coherence of the
wave-packet, which is associated with the spread of the wave packet in energy.
The two contributions can be addressed separately in the weak back-scattering
regime, when the auto-correlation noise depends only on the coherence. Analysis
of shot noise in terms of these contributions allows us, in particular, to
predict that no individual travelling particles with a real wave function, such
as Majorana fermions, can be created in the Fermi sea in a clean manner, that
is, without accompanying electron-hole pairs.
