Supersymmetry of the Quantum Rotor

DOI10.1142/9789813228887_0015zbMATH Open1411.33016arXiv1607.06967OpenAlexW2478274943MaRDI QIDQ5377719

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Publication date: 27 May 2019

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Abstract: The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3{)}_{-1}$, an anticommutator version of $so(3)$. The subduced representation of $so(3{)}_{-1}$ on the space of spherical harmonics with total angular momentum $j$ is constructed and found to decompose into two irreducible components. Two natural bases for the irreducible representation spaces of $so(3{)}_{-1}$ are introduced and their overlap coefficients prove expressible in terms of orthogonal polynomials of a discrete variable called anti-Krawtchouk polynomials.

Full work available at URL: https://arxiv.org/abs/1607.06967

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