Bogoliubov transformation for distinguishable particles

Details Bogoliubov transformation for distinguishable particles Bogoliubov transformation for distinguishable particles

1999-11-10

arxiv.org/abs/cond-mat/9911150v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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.

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