Superintegrable Systems with Arbitrary Spin
Keywords:superintegrability, supersymmetry, spin, anomalous interaction
Superintegrable quantum mechanical systems with spin are presented. These systems admit a generalized Laplace–Runge–Lenz vector and possess the dynamical symmetry with respect to group SO(4) for bound states. Our discussion is restricted mainly to 2d and 3d systems, but a special class of arbitrary dimension systems is presented as well.
O. Ragnisco and D. Riglioni, SIGMA 6, 097 (2010).
P. Winternitz, Ya.A. Smorodinsky, M. Uhli˘r, and I. Fri˘s, Sov. J. Nucl. Phys. 4, 444 (1967).
W. Miller, jr., S. Post, and P. Winternitz, arXiv:1309.2694.
W. Pauli, Z. f¨ur Physik 36, 336 (1926).
D. Zwanziger, Phys. Rev. 176, 1480 (1968).
H. McIntosh and A. Cisneros, J. Math. Phys. 11, 896 (1970).
E. D'Hoker and L. Vinet, Phys. Rev. Lett. 55, 1043 (1986).
A.G. Nikitin, J. Phys. A 45, 485204 (2012).
J.-F. D’esilets, P. Winternitz, and I. Yurdusen, J. Phys. A 45, 475201 (2012).
A. Kirchberg, J.D. L¨ange, P.A.G. Pisani, and A. Wipf, arXiv:hep-th/0208228v2.
A.G. Nikitin, arXiv: 1308.4279.
G.P. Pron'ko and Y.G. Stroganov, JETP 45, 1075 (1977).
A.G. Nikitin, J. Phys. A: 45, 225205 (2012).
D. Martinez, V.D. Granados, and R.D Mota, Phys. Lett. A 350, 31 (2006).
A.G. Nikitin, J. Phys. A 46, 256204 (2013)
E.C.G. Sudarshan, N. Mukunda, and L. O'Raifeartaigh, Phys. Lett. 19, 322 (1965).
G.P. Pronko, J. Phys. A 40, 13331 (2007).
A.G. Nikitin and O. Kuriksha, Commun. Nonlinear Sci. Numer. Simulat. 17, 4585 (2012);
A.G. Nikitin and Oksana Kuriksha, Phys. Rev. D 86, 025010 (2012).
A.G. Nikitin, J. Math. Phys. 53, 122103 (2012).
A.G. Nikitin, J. Phys. A 46, 256204 (2013).
J. Niederle and A.G. Nikitin, J. Math. Phys. 40, 1280 (1999).
W.I. Fushchich and A.G. Nikitin, J. Math. Phys. 38, 5944 (1997).
J. Beckers, N. Debergh, and A.G. Nikitin, Int. J. Theor. Phys. 36, 1991 (1997).
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