Revista Matemática Iberoamericana
Full-Text PDF (488 KB) | Table of Contents | RMI summary
Poincaré-Invariant Structures in the Solution Manifold of a Nonlinear Wave Equation
Irving E. Segal (1)(1) Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA 02139-4307, CAMBRIDGE, UNITED STATES
The solution manifold $M$ of the equation $\phi + g\phi^3 = 0$ in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on $M$ that is Poincaré invariant. In the vanishing curvature case $g = 0$ the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal space-time.
No keywords available for this article.