Krusch, Steffen (2013) Quantum lump dynamics on the twosphere. Communications in Mathematical Physics, 322 (1). pp. 95126. ISSN 00103616. (doi:10.1007/s0022001317301) (KAR id:31261)
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Official URL http://xxx.lanl.gov/abs/arXiv:1204.6203 
Abstract
It is well known that the lowenergy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static nsolitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. BornOppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the nsoliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the twosphere. Here M_1=TSO(3), a noncompact kaehler 6manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spinisospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spinisospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged lowlevel spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.
Item Type:  Article 

DOI/Identification number:  10.1007/s0022001317301 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry Q Science > QC Physics > QC20 Mathematical Physics 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Steffen Krusch 
Date Deposited:  04 Oct 2012 13:57 UTC 
Last Modified:  16 Nov 2021 10:09 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/31261 (The current URI for this page, for reference purposes) 
Krusch, Steffen:  https://orcid.org/0000000331268635 
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