# Tag Info

## New answers tagged many-body

0

You could check the works of Emilio del Giudice, Giuliano Praparata et al. The second one in particular is been involved in the study of coherence effects in quantum field theory, in particular in quantum chromo dynamics and quantum electrodynamics. In this article ...

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The assumption is, that the spin $S$ is a large parameter. A conjecture that is apparently not valid for $S=1/2$. The expansion is in $1/S$, which is assumend to be close to zero. $$S^+_j = \sqrt{2S-n_j}a^\dagger_j = \sqrt{2S}\sqrt{1-\frac{n_j}{2S}}a^\dagger_j\approx\sqrt{2S}\cdot\left(1-\frac{n_j}{4S}\right)a^\dagger_j$$ The second term, being of order ...

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The hamiltonian $$H=AJ_z^2=A\left(\sum_j S_z^{(j)}\right)^2\tag1$$ is a function of the individual $z$ spin projections $S_z^{(j)}$, and all of those commute. Therefore, the eigenstates will be product states of the form $$|\Psi\rangle=|a_1\rangle\otimes\cdots\otimes|a_N\rangle,\tag2$$ where each $|a_j\rangle$ is either $|\!\uparrow\rangle$ or ...

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