## Witten's Equations

Also called the Seiberg-Witten Invariants. For a connection and a Positive Spinor ,

The solutions are called monopoles and are the minima of the functional

References

Cipra, B. A Tale of Two Theories.'' What's Happening in the Mathematical Sciences, 1995-1996, Vol. 3. Providence, RI: Amer. Math. Soc., pp. 14-25, 1996.

Donaldson, S. K. The Seiberg-Witten Equations and 4-Manifold Topology.'' Bull. Amer. Math. Soc. 33, 45-70, 1996.

Kotschick, D. Gauge Theory is Dead!--Long Live Gauge Theory!'' Not. Amer. Math. Soc. 42, 335-338, 1995.

Seiberg, N. and Witten, E. Monopoles, Duality, and Chiral Symmetry Breaking in Supersymmetric QCD.'' Nucl. Phys. B 431, 581-640, 1994.

Witten, E. Monopoles and 4-Manifolds.'' Math. Res. Let. 1, 769-796, 1994.