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A convenient formalism is developed to treat classical dynamical systems
involving $(p=2)$ parafermionic and parabosonic dynamical variables. This is
achieved via the introduction of a parabracket which summarizes the
paracommutation relations of the corresponding Green components in a unified
manner. Furthermore, it is shown that Peierls quantization scheme may be
applied to such systems provided that one uses the above-mentioned parabracket
to express the quantum paracommutation relations. Application of
the Peierls scheme also provides the form of the parafermionic and parabosonic
kinetic terms in the Lagrangian.
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