Elliptic constructions of hyperkaehler metrics II: The quantum mechanics of a Swann bundle

Abstract

The generalized Legendre transform method of Lindstrom and Rocek yields hyperkaehler metrics from holomorphic functions. Its main ingredients are sections of $\mathcal{O}(2j)$ bundles over the twistor space satisfying a reality condition with respect to antipodal conjugation on the hyperkaehler sphere of complex structures. Formally, the structure of the real $\mathcal{O}(2j)$ sections is identical to that of quantum-mechanical wave functions describing the states of a particle with spin $j$ in the spin coherent representation. We analyze these sections and their SO(3) invariants and illustrate our findings with two Swann bundle constructions.

25 pages, 3 figures

References in corpus (2)

• A note on conformal symmetry in projective superspace
• Elliptic constructions of hyperkaehler metrics III: Gravitons and Poncelet polygons

Cited by in corpus (3)

• Elliptic constructions of hyperkaehler metrics I: The Atiyah-Hitchin manifold
• A note on conformal symmetry in projective superspace
• Elliptic constructions of hyperkaehler metrics III: Gravitons and Poncelet polygons