Evaluate the following Greens functions for a free Fermi gas.
Take the averagewith respect to a state characterized
by a distribution function
Evaluate the Fourier Transform in space and time of the following Greens functions.
a)
b)
c)
d)
e)
f)
g)
Compare them with the Fourrier transfomr of the Matsubara Greens function.
.