تقرير
Algebraic structure of the renormalization group in the renormalizable QFT theories
| العنوان: | Algebraic structure of the renormalization group in the renormalizable QFT theories |
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| المؤلفون: | Kataev, Andrei, Stepanyantz, Konstantin |
| سنة النشر: | 2024 |
| المجموعة: | High Energy Physics - Phenomenology High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, High Energy Physics - Phenomenology |
| الوصف: | We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the commutation relations of the Witt algebra and, therefore, form its subalgebra. The commutation relations are also written for the more general case when finite renormalizations are made for both the coupling constant and matter fields. We also construct the generator of the Abelian subgroup corresponding to the changes of the renormalization scale. The explicit expressions for the renormalization group generators are written in the case when they act on the $\beta$-function and the anomalous dimension. It is explained how the finite changes of these functions under the finite renormalizations can be obtained with the help of the exponential map. Comment: 15 pages, minor clarifications, the version accepted for publication in the memorial V.A.Rubakov volume of International Journal of Modern Physics A |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.15856 |
| رقم الأكسشن: | edsarx.2404.15856 |
| قاعدة البيانات: | arXiv |
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