Superintegrable systems with spin and second-order tensor and pseudo-tensor integrals of motion

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YURDUŞEN İ., TUNCER O. O., Winternitz P.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.54, no.30, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 30
  • Publication Date: 2021
  • Doi Number: 10.1088/1751-8121/ac0a9e
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH
  • Keywords: superintegrable systems, spin, tensor integrals of motion, pseudo-tensor integrals of motion, 3RD-ORDER INTEGRALS, EXACT SOLVABILITY, QUANTUM, POTENTIALS, SYMMETRIES, PARTICLE
  • Hacettepe University Affiliated: Yes


We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems which allow additional tensor and pseudo-tensor integrals of motion that are second-order matrix polynomials in the momenta. Previously we found all the scalar, pseudo-scalar, vector and axial vector integrals of motion. No non-obvious tensor integrals exist. However, nontrivial pseudo-tensor integrals do exist. Together with our earlier results we give a complete list of such superintegrable Hamiltonian systems allowing second-order integrals of motion.