# Tagged Questions

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### Solving the BCS Hamiltonian via the Bogoliubov Transformation

I was doing a calculation in Giamarchi's Introduction to Many Body Physics, chapter 3, on BCS theory and second quantization, and ran into some confusion with the BCS Hamiltonian. The pdf is here for ...
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It is common to see people do a change of sign in the so called electron-hole representation, namely, $$b^{\dagger}_{-k}=a_{v,k}$$ similar argument also seen in 1992 mattuck's book "guide to ...
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### Second Quantization - Texts

I am trying to familiarize myself with the ideas of Second Quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. There ...
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### How to evaluate spin operators in second quantization for spin symmetry-broken Slater determinants?

Suppose we have the following Slater determinant: $$| \Psi \rangle = \prod \limits_{i,i'} a^+_{i\alpha} a^+_{i'\beta} | \rangle$$ where $a^+_{i\alpha}$ creates an electron ...
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### Why is the Wick contraction in HFB or BCS equal to a single-particle density?

I'm trying to understand how in Hartree-Fock-Bogoliubov (HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem". ...
### Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?
One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits  \delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr] = ...