Timeline for The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics
Current License: CC BY-SA 2.5
5 events
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| Feb 12, 2010 at 10:26 | comment | added | José Figueroa-O'Farrill | I think it depends on what you mean by supersymmetry. If you mean simply that the spectrum arranges itself into representations of a Lie superalgebra, then sure. But then there are (approximate) supersymmetries in nuclear physics already. I am slightly more conservative and insist that for a system to be supersymmetric, the superalgebra ought to be a "spacetime" superalgebra (or in statistical mechanical systems a "euclidean" superalgebra). This is the case for the Josephson junction, where you have a conformal superalgebra acting conformally on the two-dimensional space. | |
| Feb 12, 2010 at 9:54 | comment | added | Igor Khavkine | For the record, I believe that one of the simplest (if not the simplest) quantum system with supersymmetry is a non-relativistic spin-1/2 particle confined in a 1-d harmonic potential. This system can most likely be realized experimentally by placing an electron in a special magneto-optical trap. | |
| Feb 9, 2010 at 8:10 | comment | added | Orbicular | Your comments concerning classical representation theory are true, obviously. Please keep in mind that the question concerned "the use of Quantum Groups and their representations to Physicists", so Wigner's and Gell-Mann's results do not apply. Neither supersymmetry nor string theory have been observed up to this point. On the contrary, new (questionable) hypotheses have been introduced (like superpartners and additional space-time dimensions). These hypotheses introduce new degrees of freedom, making the observability (and falsifiability) at least more difficult! | |
| Feb 9, 2010 at 2:42 | comment | added | B. Bischof | thanks so much for this answer. I will need some time to look it over, but the first reading was very interesting . | |
| Feb 8, 2010 at 23:51 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |