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  • Regularization schemes of the pairing field

Regularization schemes of the pairing field · Changes

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Update Regularization schemes of the pairing field authored Jan 17, 2026 by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Regularization-schemes-of-the-pairing-field.md
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......@@ -49,7 +49,7 @@ For more info, see [arXiv:1008.3933](https://arxiv.org/abs/1008.3933).
```
The effective coupling constant is computed according to the prescription:
```math
\dfrac{1}{g_{\textrm{eff}}}=\dfrac{1}{g_0} - \dfrac{m}{2\alpha_+}\dfrac{K}{2\hbar^2\pi^2 dx},
\dfrac{1}{g_{\textrm{eff}}}=\dfrac{1}{g_0} - \dfrac{m}{2\alpha_+}\dfrac{K}{2\hbar^2\pi dx},
```
where $`K=2.442 75`$ is a numerical constant. In this formula, we assume that all states contribute to the densities. Physically, it means that we take into account states up to the maximal value of energy set by the lattice, which is of the order $`E_c\approx 3\frac{\hbar^2\pi^2}{2mdx^2}`$ (assuming that $`dx=dy=dz`$).
*Note*: when working with this renormalization scheme value of tag `ec` will be ignored.
......
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