Hidden symmetry of hyperbolic monopole motion
نویسندگان
چکیده
Hyperbolic monopole motion is studied for well separated monopoles. It is shown that the motion of a hyperbolic monopole in the presence of one or more fixed monopoles is equivalent to geodesic motion on a particular submanifold of the full moduli space. The metric on this submanifold is found to be a generalisation of the multi-centre Taub-NUT metric introduced by LeBrun. The one centre case is analysed in detail as a special case of a class of systems admitting a conserved Runge-Lenz vector. The two centre problem is also considered. An integrable classical string motion is exhibited. [email protected] [email protected]
منابع مشابه
Hyperbolic monopoles, JNR data and spectral curves
A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. Thes...
متن کاملTetrahedral and Cubic Monopoles
Using a numerical implementation of the ADHMN construction, we compute the fields and energy densities of a charge three monopole with tetrahedral symmetry and a charge four monopole with octahedral symmetry. We then construct a one parameter family of spectral curves and Nahm data which represent charge four monopoles with tetrahedral symmetry, which includes the monopole with octahedral symme...
متن کاملNon-Commutative Corrections to the MIC-Kepler Hamiltonian
Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and parabolic coordinates. Despite the fact that there is no simple analytic expression for non-commutative perturbative corrections to the MICKepler spectrum, there is a term that gives rise to the linear Stark effect which didn’t exist in the standard hydr...
متن کاملFree conical dynamics: charge-monopole as a particle with spin, anyon and nonlinear fermion-monopole supersymmetry
ṙ 2 2v + v 2 with einbien v [2]. Amazingly, this dynamical symmetry relates the mechanisms of supernova explosion and plasma implosion [3], and the theoretical explanation of such an intriguing similarity finds its roots in the symmetry properties of the fluid dynamic equations [4]. Since the charge-monopole (CM) system is characterized by the same dynamical SL(2, R) symmetry [5], this indicate...
متن کاملMonopole Scattering with a Twist
By imposing certain combined inversion and rotation symmetries on the rational maps for SU(2) BPS monopoles we construct geodesics in the monopole moduli space. In the moduli space approximation these geodesics describe a novel kind of monopole scattering. During these scattering processes axial symmetry is instantaneously attained and, in some, monopoles with the symmetries of the regular soli...
متن کامل