Justification ofc-Number Substitutions in Bosonic Hamiltonians

摘要: The validity of substituting a c-number z for the k=0 mode operator a(0) is established rigorously in full generality, thereby verifying one aspect Bogoliubov's 1947 theory. This substitution not only yields correct value thermodynamic quantities such as pressure or ground state energy, but also |z|(2) that maximizes partition function equals true amount condensation presence gauge-symmetry-breaking term. point had previously been elusive.