Equivalence of Helicity and Euclidean Self-Duality for Gauge Fields


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April 7, 2020 10:00 am - 11:00 am
via Zoom Video Conferencing

Leonard Gross - Cornell University

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].
[1] https://doi.org/10.1016/j.nuclphysb.2019.114685