Minimum Polynomial for Single-Mode Parabose Parasupercharge and Hamiltonian

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We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y) satisfies the homogeneity ∀λ ∈ ℝ, φ(λx, λ2y) = λnφ(x,y), then the parafermionic order pf is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x,y) is equivalent to the parasuperconformality of Q and H. The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle.

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