MICZ-Kepler problems in all dimensions
نویسنده
چکیده
The Kepler problem is a physical problem about two bodies which attract each other by a force proportional to the inverse square of the distance. The MICZ-Kepler problems are its natural cousins and have been previously generalized from dimension three to dimension five. In this paper, we construct and analyze the (quantum) MICZ-Kepler problems in all dimensions higher than two.
منابع مشابه
ar X iv : m at h - ph / 0 50 70 28 v 1 1 2 Ju l 2 00 5 The MICZ - Kepler problems in all dimensions
The Kepler problem is perhaps the most well-known physics problem in the last three centuries. The MICZ-Kepler problems are its natural cousins. While the Kepler problem exists obviously in high dimensions, only the 5-dimensional analogues of the MICZ-Kepler problems were discovered previously. In this paper, we demonstrate that the quantum MICZ-Kepler problems do exist in all dimensions greate...
متن کاملGeneralized Micz - Kepler Problems and Unitary Highest Weight
For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem with magmatic charge μ = 0 or 1/2 has an Spin(2, 2n+ 1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification d...
متن کاملar X iv : 0 71 1 . 10 37 v 1 [ m at h - ph ] 7 N ov 2 00 7 Generalizations of MICZ - Kepler system
We discuss the generalizations of the MICZ-Kepler system (the system describing the motion of the charged particle in the field of Dirac dyon), to the curved spaces, arbitrary potentials and to the multi-dyon background. The integrable system describing the motion of the charged particle in the field of Dirac dyon (magnetic monopole carrying the electric charge) has been suggested independently...
متن کاملar X iv : 0 70 4 . 29 36 v 3 [ m at h - ph ] 9 A ug 2 00 7 GENERALIZED MICZ - KEPLER PROBLEMS AND UNITARY HIGHEST WEIGHT MODULES – II
For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...
متن کاملar X iv : 0 70 4 . 29 36 v 2 [ m at h - ph ] 2 4 Ju l 2 00 7 GENERALIZED MICZ - KEPLER PROBLEMS AND UNITARY HIGHEST WEIGHT MODULES – II
For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...
متن کامل