Abstract:
Statistical mechanics is related to quantum mechanics at the root. Classical statistical mechanics
has several problems such as ergodic hypothesis, Gibbs factor, necessity of Planck constant,
principle of a priori probability and correspondence between classical and quantum related to
temperature.
Our purpose is to find one of the argument which lead from quantum mechanics to statistical
mechanics. In this research, microcanonical and canonical ensemble are derived from stationary
Schrödinger equation for boson and fermion. The important aims are to realize perfect
decoherence and a priori probability for isolated system. However, these require special condition
for entanglement of stationary. For the sake of generation such entanglement, it is necessary to
introduce interactions between the particles. The concept of classical ideal gas also includes weak
interactions which disappear after carrying out thermodynamic limit. Thus, this discussion starts
from determination of interaction Hamiltonian. The hidden gauge structure plays central role,
here. We adopt the phase operator of special type as introduction of gauge transformation. This
phase operator come into play abelian gauge field. We set coupling constant of this interaction to
vanishing at thermodynamic limit. By doing this, the situation which is similar to random phase
appear, moreover, perfect decoherence for isolated system and a priori probability is realized.
Once the above is accomplished, it is possible that a microcanonical ensemble for isolated system
is constructed. Furthermore, we constitute canonical ensemble theory from thus obtained
microcanonical ensemble theory.