  We examine the weakly interacting atoms in an ultracold Fermi gas leading to
a state of macroscopic coherence, from a theoretical perspective. It has been
shown that this state can be described as a fermionic coherent state. These
coherent states are the eigenstates of fermionic annihilation operators, the
eigenvalues being anti-commuting numbers or Grassmann numbers. By exploiting
the simple rules of Grassmann algebra and a close kinship between relations
evaluated for more familiar bosonic fields and those for fermionic fields, we
derive the thermodynamic limit, the spontaneous symmetry breaking and the
quasi-particle spectrum of the fermionic system.
