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The representations of the oscillator group

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Abstract

Using the Mackey theory of induced representations all the unitary continuous irreducible representations of the 4-dimensional Lie groupG generated by the canonical variables and a positive definite quadratic ‘hamiltonian’ are found. These are shown to be in a one to one correspondence with the orbits underG in the dual spaceG′ to the Lie algebraG ofG, and the representations are obtained from the orbits by inducing from one-dimensional representations provided complex subalgebras are admitted. Thus a construction analogous to that ofKirillov andBernat gives all the representations of this group.

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References

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Authors and Affiliations

  1. Physics Department Imperial College, S.W. 7, London

    R. F. Streater

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  1. R. F. Streater
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The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research OAR through the European Office Aerospace Research, United States Air Force.

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Streater, R.F. The representations of the oscillator group. Commun.Math. Phys. 4, 217–236 (1967). https://doi.org/10.1007/BF01645431

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  • DOI: https://doi.org/10.1007/BF01645431

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