  The mathematical methods that have been used to analyze the statistical
properties of boson fields, and in particular the coherence of photons in
quantum optics, have their counterparts for Fermi fields. The coherent states,
the displacement operators, the P-representation, and the other operator
expansions all possess surprisingly close fermionic analogues. These methods
for describing the statistical properties of fermions are based upon a
practical calculus of anti-commuting variables. They are used to calculate
correlation functions and counting distributions for general systems of
fermions.
