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Geometric Quantization of the 1 : 1 Oscillator

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Abstract

We study geometric quantization of the 1 : 1 in terms of a singular real polarization given by fibres of its energy momentum map.

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Notes

  1. In representation theory, shifting operators are called ladder operators. The corresponding operators in quantum field theory are called the creation and annihilation operators.

  2. Our discussion is similar to the standard treatment of quantizing the 2d harmonic oscillator in Messiah [4, p.451-456].

  3. This is reminiscent of half integer and integer spin, see Messiah [4, p.544–549].

References

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Authors and Affiliations

  1. University of Calgary, Calgary, Alberta, Canada

    Richard Cushman & Jędrzej Śniatycki

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  1. Richard Cushman
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  2. Jędrzej Śniatycki
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Correspondence to Richard Cushman.

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Cushman, R., Śniatycki, J. Geometric Quantization of the 1 : 1 Oscillator. Qual. Theory Dyn. Syst. 19, 81 (2020). https://doi.org/10.1007/s12346-020-00417-x

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  • DOI: https://doi.org/10.1007/s12346-020-00417-x

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