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Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System

Michael Martin Nieto·D. Rodney Truax
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Abstract

As an aid to understanding the {\it displacement operator} definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the {\it ladder-operator or minimum-uncertainty} definitions of squeezed states are equivalent to an extent displacement-operator definition. We exemplify this in a setting where there are operators satisfying $[A, A^{\dagger}] = 1$, but the $A$'s are not necessarily the Fock space $a$'s; the multiboson system. It has been previously observed that the ground state of a system often can be shown to to be a coherent state. We demonstrate why this must be so. We close with a discussion of an alternative, effective definition of displacement-operator squeezed states.

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Michael Martin Nieto, D. Rodney Truax. 1996-05-22. Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System. https://doi.org/10.1002/prop.2190450204

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