Quantization of Fields of Arbitrary Spin

  • Bill Cox

    Student thesis: Doctoral ThesisDoctor of Philosophy


    The search for relativistic field equations for
    elementary particles of arbitrary spin is a long standing
    problem of Quantum Field Theory. Although much work has been
    done on relativistic field theories describing fields with
    various mass-spin spectra, little has been done on picking
    out those theories which are quantizable, that is, those for
    which a particle interpretation exists which is consistent
    with the basic postulates of quantum theory.
    In this thesis we examine theories based on the
    relativistic field equation

    (Lμϑμ + X)Ψ = 0.

    The condition for ecahi tata on is expressed in terms of certain
    positive definiteness requirements on the eigenvectors corresponding
    to the non-zero eigenvalues of Lo. By restricting the.
    discussion to a specific type of theory, in which spin states
    are not repeated, these positive definiteness requirements are
    expressed in terms of certain simple trace conditions. A
    systematic procedure for finding representations of lo for
    quantizable theories is given, and illustrated in the case of
    spin 0,1,2 fields. In this procedure use is made of graphs
    depicting the representations of the Lorentz Group according
    to which % transforms ina relativistic field theory. Some
    simple results of graph theory are applied to develop the theory
    and also to discuss the properties of the Lo matrix. Further
    possibilities of this graphical approach are briefly discussed.
    Date of Award1972
    Original languageEnglish


    • Quantization
    • fields
    • arbitrary spin

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