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Physics

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  • $\begingroup$ Yes, thanks. That's what I concluded eventually. But what irks me (and the reason for the whole long exchange above) is that almost everyone else doesn't understand the Fock space (with single particle Hilbert space of dim $M$) is isomorphic to the tensor product of $M$ orbital spaces. One can see this from looking at the dimension of the Hilbert spaces - both are $2^M$, and one has a 1-1 between the two spaces, so they are isomorphic! That implies that one can actually decompose the Fock space into a tensor product - except that because this isomorphism only works for the full spaces, $\endgroup$ Commented Sep 21, 2013 at 5:32
  • $\begingroup$ one cannot decompose the singlet wavefunction into a tensor product as $c_a^\dagger | 0 \rangle \otimes c_b^\dagger | 0 \rangle$ and represent it as some $f(x_1) \otimes g(x_2)$. $\endgroup$ Commented Sep 21, 2013 at 5:35