Seminar Spectral Theory and PDE

Seminar Spectral Theory and PDE, May 30, 17:00

Speaker: Dmitrii Shirokov. National Research University Higher School of Economics, Russia

Title: On Constant Solutions of Su(2) Yang-Mills Equations

Place: Pontificia Universidad Católica, Facultad de Matemáticas (Campus San Joaquin), Sala 2

We present all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space of arbitrary finite dimension. We use the singular value decomposion method and the method of two-sheeted covering of orthogonal group by spin group to do this. Using hyperbolic singular value decomposition, we solve the same problem in arbitrary pseudo-Euclidean space. The case of Minkowski space is discussed in details. Nonconstant solutions of the Yang-Mills equations are considered in the form of series of perturbation theory.