Witten's gauge field equations and an infinite-dimensional Grassmann manifold (Q1097566)

Witten's gauge field equations [\textit{E. Witten}, Phys. Lett. B 77, 394- 398 (1978)] are rewritten as motions on infinite-dimensional Grassmann manifolds. The solutions are investigated by methods, which are analogous to Takasaki's work on self-dual Yang-Mills fields [\textit{K. Takasaki}, Commun. Math. Phys. 94, 35-59 (1984; Zbl 0552.58036)]. The appearance of two spectral parameters (instead of one) requires the initial data to satisfy a system of differential equations. On this condition, an existence - and uniqueness - theorem for the initial value problem is proven.