On the symplectic structure of instanton moduli spaces

Details On the symplectic structure of instanton moduli spaces On the symplectic structure of instanton moduli spaces

2008-12-29

arxiv.org/abs/0812.4918v3

Mathematics

Symplectic Geometry

couple of misprints corrected

Scientific paper

We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R^4. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero-Moser spaces to the instanton moduli spaces.

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