  There are two formulations at non-zero chemical potential; one is the
formulation that a Lagrangian includes a chemical potential, the other is the
formulation that a Lagrangian does not include a chemical potential. The
existence of two formulations makes a calculation complicated. The results from
those formulations are not corresponding directly. This discrepancy exists in
the imaginary time formalism and the real time formalism. However, since this
is essentially caused by a difference of a frequency, the discrepancy vanishes
by modifying the Fourier transform. We show a calculational procedure with a
spectral function to understand this.
