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Generic example of algebraic bosonisation

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Abstract

Two identical non-interacting fermions in a three-dimensional harmonic oscillator well are bosonised exactly according to a recently developed general algebraic scheme. Rotational invariance is taken into account within the scheme for the first time. The example is generic for the excitation spectra of finite systems, in particular for the appearance of bands in spectra. A connection to the formalism of the fractional quantum Hall effect is pointed out.

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Notes

  1. 1.

    The Euler bosons are a complete basis of symmetric functions in each direction separately, while \(\varPsi _1\varPsi _2\) factorizes into antisymmetric functions across the two directions.

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Acknowledgements

This work was supported by the Croatian Science Foundation under Project No. IP-2018-01-7828 and University of Zagreb Support Grant 20283207. KR thanks the Croatian Physical Society for a travel grant.

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Correspondence to D. K. Sunko.

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Rožman, K., Sunko, D.K. Generic example of algebraic bosonisation. Eur. Phys. J. Plus 135, 30 (2020). https://doi.org/10.1140/epjp/s13360-019-00015-0

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