The known approximation schemes for the solution of the Wetterich exact renormalization group (RG) equation are critically reconsidered, and a new truncation scheme is proposed. In particular, the equations of the derivative expansion up to the ∂ 2 order for a scalar model are derived in a suitable form, clarifying the role of the off-diagonal terms in the matrix of functional derivatives. The natural domain of validity of the derivative expansion appears to be limited to small values of q / k in the calculation of the critical two-point correlation function, depending on the wave-vector magnitude q and the infrared cut-off scale k . The new approximation scheme has the advantage to be valid for any q / k , and, therefore, it can be auspicious in many current and potential applications of the celebrated Wetterich equation and similar models. Contrary to the derivative expansion, derivatives are not truncated at a finite order in the ...

中文翻译：

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Wetterich方程求解的一种新方法及其应用。

严格地重新考虑了Wetterich精确重整化群（RG）方程解的已知近似方案，并提出了一种新的截断方案。尤其是，标量模型的导数展开式直至∂2阶的方程式以合适的形式导出，阐明了对角项在功能导数矩阵中的作用。在计算临界两点相关函数时，取决于波矢量幅值q和红外截止尺度k，导数展开的有效性的自然域似乎仅限于q / k的较小值。新的近似方案具有对任何q / k都有效的优点，因此，在著名的Wetterich方程和类似模型的许多当前和潜在应用中，它都是吉利的。