  The Bogoliubov transformation is generally derived in the context of
identical bosons with the use of ``second quantized'' a and $a^{\dagger}$
operators (or, equivalently, in field theory). Here, we show that the
transformation, together with its characteristic energy spectrum, can also be
derived within the Hilbert space of distinguishable particles, obeying
Boltzmann statistics; in this derivation, ordinary dyadic operators play the
role usually played by the a and $a^{\dagger}$ operators; therefore, breaking
the symmetry of particle conservation is not necessary.
