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On the general linear (Bogoliubov-) transformation for bosons

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Zeitschrift für Physik B Condensed Matter

Abstract

Using a Baker-Campbell-Hausdorff formula for the disentangling of exponential operators, a simple straight-forward derivation of Bogoliubov-transformation matrix elements could be given by elementary algebra. Recent much more complicated derivations by means of hypergeometric functions are simplified considerably. Matrix elements and their generating functions are new for the general linear transformation for bosons. The surprising result of Aronsonet al., that the linear transformation matrix element is equivalent to the rotation matrix element is discussed in the framework of the coupled boson theory of angular momentum. Possible applications of the formalism for quantum optics and for nuclear models are sketched briefly.

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Authors and Affiliations

  1. Institut für Physikalische Chemie, Technische Universität Braunschweig, Gaußstraße 23, D-3300, Braunschweig, Federal Republic of Germany

    W. Witschel

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  1. W. Witschel
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Witschel, W. On the general linear (Bogoliubov-) transformation for bosons. Z Physik B 21, 313–318 (1975). https://doi.org/10.1007/PL00020756

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  • DOI: https://doi.org/10.1007/PL00020756

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