Timeline for Classical geometric interpretation of spinors
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2011 at 11:02 | comment | added | Spiro Karigiannis | @Benjamin: I think you said it best yourself, that you should think of spinors as "square roots" of classical geometry. There is another notion from calibrated geometry that explains how a calibration (such as the Kahler form) is a "square" of a spinor (see the book by Reese Harvey). Also, manifolds which admit spinor fields that satisfy a nice differential equation (harmonic spinors, Killing spinors, etc) tend to have nice properties on their Riemannian metrics (Ricci-flat, Einstein, etc) | |
| Jun 2, 2011 at 4:57 | comment | added | Benjamin | I would like to add that spinor geometry plays a very important role in the Atiyah-Singer index theorem (I could make this statement more precise), so perhaps this gives other people a lead to my question, since a lot of spinor geometry is used in this theorem. | |
| Jun 2, 2011 at 4:52 | comment | added | Benjamin | @r0b0t: Thanks, I forgot this! To define the square root of the Laplace-Beltrami operator I need spinors to get the Dirac operator. More generally my teacher always said that spinors are the "square root" of usual geometry. I also know that Cartan thought like this, and it seems very natural to him. | |
| Jun 2, 2011 at 4:42 | vote | accept | Benjamin | ||
| Jun 2, 2011 at 4:58 | |||||
| Jun 1, 2011 at 23:51 | history | answered | Vít Tuček | CC BY-SA 3.0 |