# Online: Seminar, Leonard Gross (Cornell University), Equivalence of Helicity and Euclidean Self-Duality for Gauge Fields #### calendar\_today Date and Time **April 7, 2020** 10:00AM - 10:00AM EDT #### pin\_drop Location **Zoom** ![Leonard Gross](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/gross.jpg?itok=0ahtC4gK) **Location:** Zoom [https://harvard.zoom.us/j/779283357&nbsp](https://harvard.zoom.us/j/779283357 ); **Time:** Tuesday, April 7, 2020, 10:00 AM (Eastern US), 16:00 (Central Europe), 22:00 (China) **Title:** Equivalence of Helicity and Euclidean Self-Duality for Gauge Fields **Abstract:** 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 \\(\\mathbb 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** \[1\] **Additional Ways to Join** Join by telephone (use any number to dial in) +1 929 436 2866 +1 312 626 6799 +1 669 900 6833 +1 253 215 8782 +1 301 715 8592 +1 346 248 7799 +41 43 210 70 42 +41 43 210 71 08 +41 22 591 00 05 +41 22 591 01 56 +41 31 528 09 88 +31 20 794 6520 +31 20 794 7345 +31 20 241 0288 +31 20 794 0854 +31 20 794 6519 +65 3165 1065 +65 3158 7288 +33 1 7095 0350 +33 7 5678 4048 +33 1 7037 2246 +33 1 7037 9729 +33 1 7095 0103 +49 30 5679 5800 +49 695 050 2596 +49 69 7104 9922 +45 32 72 80 11 +45 89 88 37 88 +45 32 70 12 06 +45 32 71 31 57 +45 32 72 80 10 400 669 9381 China Toll-free 400 616 8835 China Toll-free 0 800 561 252 Switzerland Toll-free 0 800 002 622 Switzerland Toll-free 0 800 220 0040 Netherlands Toll-free 0 800 022 1954 Netherlands Toll-free 800 852 6054 Singapore Toll-free 800 101 3814 Singapore Toll-free 0 805 082 588 France Toll-free 0 800 940 415 France Toll-free 0 800 1800 150 Germany Toll-free 0 800 000 6954 Germany Toll-free 80 82 02 88 Denmark Toll-free 80 71 12 51 Denmark Toll-free International numbers available: One tap mobile: +19294362866,,779283357# US (New York) Join by SIP conference room system Meeting ID: 779 283 357 <779283357@zoomcrc.com> Share on:- [ Facebook ](#) - [ Twitter ](#) - [ Linkedin ](#) Save: [ Add to calendar calendar\_today ](https://mathpicture.fas.harvard.edu/node/1490310/event-feed.ics) Copy link link