Witten's gauge field equations and an infinite-dimensional Grassmann manifold
type: Item
instance of: scholarly article
title: Witten's gauge field equations and an infinite-dimensional Grassmann manifold
zbMATH Open document ID: 0635.58038
DOI: 10.1007/BF01221403
author: Norio Suzuki
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4034727
zbMATH Keywords: Witten's gauge field equations
zbMATH Keywords: self-dual Yang-Mills fields
zbMATH Keywords: spectral parameters
zbMATH Keywords: initial value problem
reviewed by: Volker Perlick
MaRDI profile type: Publication
cites work: Structure of the solution space of Witten's gauge-field equations
cites work: On the structure of solutions to the self-dual Yang-Mills equations
cites work: A new approach to the self-dual Yang-Mills equations
description: scientific article; zbMATH DE number 4034727