Timeline for In quantum dynamical simulations, what is the symmetric (Riemannian) analog of a Poisson bracket?
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| Jun 1, 2011 at 22:41 | comment | added | Theo Johnson-Freyd | @John: You're welcome. I am definitely not familiar with the chemistry literature, and for me "geometry" and "algebra" are very close. I expect that the approaches are essentially equivalent if phrased correctly; coming at the question as a category theorist has led me to see the similarities between bosonic and fermionic constructions, but of course there are also qualitative differences. | |
| Jun 1, 2011 at 18:24 | comment | added | John Sidles | Thank you Theo, for this graceful answer ... which will take me a considerable time to digest. The chemistry literature had been pointing me in a direction that was more geometric and less algebraic, namely, that the natural varieties on which to pullback fermionic trajectories are the varieties that chemists use, which they call Slater determininants (and their rank-$r$ secant joins). Now, it seems (to me) that this geometric approach should be wholly equivalent to your algebraic approach... but it will take awhile to appreciate how this works. Meanwhile, sincere thanks are extended. | |
| Jun 1, 2011 at 14:42 | history | answered | Theo Johnson-Freyd | CC BY-SA 3.0 |