  In the standard theory of superconductivity a quasiparticle excitation
changes the energy of the system by the quasiparticle energy. But the number of
excitations determine also the gap energy which further determines the energy
of the condensate and the energy spectrum of quasiparticles. Such extra
contributions to the total energy of the system--which are not taken into
account in the standard formalism--led us to a redefinition of the
quasiparticle energies and of the quasiparticle populations by the usual method
of the maximization of the superconductor partition function. The result of
this correction is a critical temperature which is lower than the BCS critical
temperature and a finite jump of the energy gap at the phase transition. The
discontinuity of the energy gap at the critical temperature marks a first order
phase transition which is also in disagreement with the standard BCS
interpretation. The fact that the standard BCS formalism is theoretically
inconsistent is revealed in the calculation of the heat capacity and of the
internal energy. These inconsistencies are removed in our formulation.
  The purpose of our paper is not to adjust the theory to better describe the
phenomenology of superconductivity, but to reevaluate and amend the BCS
formalism.
