Quantum Mechanics on Moduli Spaces

Abstract

It has been assumed that it is possible to approximate the interactions of quantized BPS solitons by quantising a dynamical system induced on a moduli space of soliton parameters. General properties of the reduction of quantum systems by a Born-Oppenheimer approximation are described here and applied to sigma models and their moduli spaces in order to learn more about this approximation. New terms arise from the reduction proceedure, some of them geometrical and some of them dynamical in nature. The results are generalised to supersymmetric sigma models, where most of the extra terms vanish.

19 pages, REVTeX

References in corpus (2)

• Diagrams for heat kernel expansions
• Soliton vacuum energies and the CP(1) model

Cited by in corpus (11)

• Asymptotic Interactions of Critically Coupled Vortices
• Semiclassical framed BPS states
• Level Set Method for the Evolution of Defect and Brane Networks
• On the curvature of vortex moduli spaces
• The conformally invariant Laplace-Beltrami operator and factor ordering
• The L^2 geometry of spaces of harmonic maps S^2 -> S^2 and RP^2 -> RP^2
• Dynamics of CP^1 lumps on a cylinder
• Scalar Soliton Quantization with Generic Moduli
• Supersymmetric Soliton $\sigma$-models from Non-Lorentzian Field Theories
• Soliton vacuum energies and the CP(1) model
• Quantum lump dynamics on the two-sphere