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One-loop calculation of the $\beta$-function in the modified formulation of the Yang–Mills theory
P. S. Anisimov M. V. Lomonosov Moscow State University
Abstract:
In the one-loop approximation for the modified Yang–Mills theory, we calculate contributions to the two- and three-point Green's functions of the gauge field $A_\mu$, to the Green's function of the anticommuting fields $e$ and $b$, and to the vertex function $\Gamma_{Aeb}$. We find the renormalization constants $Z_1$ and $Z_2$ and the corresponding constants $\overline Z_1$ and $\overline Z_2$ for the anticommuting fields and show that they satisfy the same equation as in the standard Yang–Mills theory. We demonstrate that the $\beta$-functions in the standard and modified theories coincide.
Keywords:
Yang–Mills theory, renormalization constant, one-loop approximation, $\beta$-function, gauge invariance.
Received: 09.02.2014
Citation:
P. S. Anisimov, “One-loop calculation of the $\beta$-function in the modified formulation of the Yang–Mills theory”, TMF, 180:3 (2014), 291–306; Theoret. and Math. Phys., 180:3 (2014), 1005–1018
Linking options:
https://www.mathnet.ru/eng/tmf8650https://doi.org/10.4213/tmf8650 https://www.mathnet.ru/eng/tmf/v180/i3/p291
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Abstract page: | 399 | Full-text PDF : | 174 | References: | 61 | First page: | 43 |
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