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Remarks on boson commutation rules

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Abstract

A group theoretical derivation is given of Bargmann's representation of the boson commutation rules in an Hilbert space of analytic functions. Several interesting problems arise in the study of the global representation of the canonical groupS p (2n, R). As a by-product we recover Laguerre-polynomials as spherical functions on the nilpotent Weyl group.

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References

  1. Bargmann, V.: Commun. Pure Appl. Math.14, 187 (1961).

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  3. Bargmann, V.: Ann. Math.48, 569 (1947).

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  4. Balian, R., C. de Dominicis, andC. Itzykson: Nucl. Phys.67, 609 (1965).

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  1. Service de Physique Théorique, Centre d'Etudes Nucléaires de Saclay, BP N° 2, 91 Gif-sur-Yvette

    C. Itzykson

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  1. C. Itzykson
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Itzykson, C. Remarks on boson commutation rules. Commun.Math. Phys. 4, 92–122 (1967). https://doi.org/10.1007/BF01645755

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  • DOI: https://doi.org/10.1007/BF01645755

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