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| bio | website | sbseminar.wordpress.com |
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| location | New York, NY | |
| age | 33 | |
| visits | member for | 1 year, 8 months |
| seen | 2 days ago | |
| stats | profile views | 8 |
I'm an assistant professor in mathematics at Indiana and an early adopter of Math Overflow. I was the first user at mathematics.SE.
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Jul 26 |
awarded | Critic |
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May 4 |
awarded | Teacher |
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Oct 16 |
comment |
direct sum of anyons? @Heidar You didn't take your nitpick far enough, as $X^{\otimes n}$ can also contains summands which don't appear in $X \otimes X$. I think the formula in my answer is right: you want to sum over all particle types. |
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Oct 16 |
comment |
direct sum of anyons? I totally rewrote the answer based on the above discussion. Hopefully it's less wrong now. |
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Oct 16 |
comment |
direct sum of anyons? @JoeFitzsimons Good point. I somehow got thrown off by 5 being a Fibonacci number as well. So the Hilbert space for an n-particle system is $\mathrm{Hom}(\phi^{\otimes n}, \phi) \oplus \mathrm{Hom}(\phi^{\otimes n}, 1)$? |
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Oct 16 |
comment |
direct sum of anyons? Ways of fusing down to a single particle is $\mathrm{Hom}(\phi \otimes \phi, \phi)$ which is indeed a vector space (unlike $\phi$ itself). This is the point I was trying to make: it's the Hom spaces that are important physically, more than the objects themselves. |
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Oct 16 |
comment |
direct sum of anyons? Look at the first two sentences of chapter 3 of Pachos's lecture notes and the last sentence on page 10. |
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Oct 16 |
comment |
direct sum of anyons? I think that equation says that the Hilbert space for a 3-particle system is 5 dimensional (which is roughly what it should be since each particle has golden ratio internal degrees of freedom). One of these states is the state that you'd get if annihilated then created them all from the vacuum. The other four correspond to ways of fusing them down to a single particle and then unfusing them back up (there are 2 ways of doing each, so 4 total). |
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Oct 16 |
comment |
direct sum of anyons? In this comment thread people seem to be referring to $\phi$ as though it were a Hilbert space. In all interesting examples it is not even a vector space. The Hilbert spaces are $\mathrm{End}(\phi)$ and $\mathrm{End}(\phi \oplus \phi)$ (which are 1 and 4 dimensional respectively). |
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Oct 16 |
answered | direct sum of anyons? |
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Oct 5 |
awarded | Citizen Patrol |
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Sep 16 |
awarded | Supporter |
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Sep 8 |
awarded | Autobiographer |
