Calendar
- 07April 7, 2020
Equivalence of Helicity and Euclidean Self-Duality for Gauge Fields
via Zoom Video Conferencing: https://harvard.zoom.us/j/779283357
Circularly polarized light (i.e. helicity) is a concept defined in terms of
plane wave expansions of solutions to Maxwell’s equations. We wish to find an analogous concept for classical and quantized Yang-Mills fields. Since the classical (hyperbolic) Yang-Mills equation is a non-linear equation, a gauge invariant plane wave expansion does not exist. We will first
show, in electromagnetism, an equivalence between the usual plane wave characterization of helicity and a characterization in terms of (anti-)self duality of a gauge potential on a half space of Euclidean R^4. The transition from Minkowski space to Euclidean space is implemented by the
Maxwell-Poisson equation. We will then replace the Maxwell- Poisson equation by the Yang-Mills-Poisson equation to find a decomposition of the Yang-Mills configuration space into submanifolds arguably corresponding to positive and negative helicity. This is a report on the paper [1].
References
[1] https://doi.org/10.1016/j.nuclphysb.2019.114685Collapsing Calabi-Yau Manifolds
via Zoom Video Conferencing: link TBA
I will report on some recent progress on the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on Calabi-Yau manifolds that admit a fibration structure, when the volume of the fibers shrinks to zero. Based on joint works with Gross-Zhang and with Hein.