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    Correspondence rules in SU (3)

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    MartinsA2018m-1b.pdf (1.200Mb)

    Date

    2018

    Author

    Nunes Martins, Alex Clesio

    Degree

    Master of Science

    Discipline

    Physics

    Subject

    Quantum mechanics
    Wigner function
    Quasi-distribution functions

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    Abstract

    In this thesis, I present a path to the correspondence rules for the generators of the su(3) symmetry and compare my results with the SU(2) correspondence rules. Using these rules, I obtain analytical expressions for the Moyal bracket between the Wigner symbol of a Hamiltonian H , where this Hamiltonian is written linearly or quadratically in terms of the generators, and the Wigner symbol of a general operator B. I show that for the semiclassical limit, where the SU(3) representation label tends to infinity, this Moyal bracket reduces to a Poisson bracket, which is the leading term of the expansion (in terms of the semiclassical parameter ), plus correction terms. Finally, I present the analytical form of the second order correction term of the expansion of the Moyal bracket.

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    http://knowledgecommons.lakeheadu.ca/handle/2453/4322

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