Physics – Mathematical Physics
Scientific paper
2008-01-15
Physics
Mathematical Physics
23 pages
Scientific paper
Contour dynamics is a classical subject both in physics and in complex analysis. We show that the dynamics provided by the L\"owner-Kufarev ODE and PDE possesses a rigid algebraic structure given by the Virasoro algebra. Namely, the `positive' Virasoro generators span the holomorphic part of the complexified vector bundle over the space of univalent functions, smooth on the boundary. In the covariant formulation they are conserved by the L\"owner-Kufarev evolution. The `negative' Virasoro generators span the antiholomorphic part. They contain a conserved term and we give an iterative method to obtain them based on the Poisson structure of the L\"owner-Kufarev evolution. The L\"owner-Kufarev PDE provides a distribution of the tangent bundle of non-normalized univalent functions, which forms the tangent bundle of normalized ones. It also gives an explicit correspondence between the latter bundle and the holomorphic eigen space of the complexified Lie algebra of vector fields on the unit circle. Finally, we give Hamiltonian and Lagrangian formulations of the motion within the coefficient body in the field of an elliptic operator constructed by means of Virasoro generators. We also discuss relations between CFT and SLE.
Markina Irina
Vasil'ev Alexander
No associations
LandOfFree
Virasoro Algebra and Löwner-Kufarev Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Virasoro Algebra and Löwner-Kufarev Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Virasoro Algebra and Löwner-Kufarev Equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-151345