Dyson-Schwinger Equations in Minimal Subtraction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917867666014208 |
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| author | Balduf, Paul-Hermann |
| author_facet | Balduf, Paul-Hermann |
| contents | We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_13684 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dyson-Schwinger Equations in Minimal Subtraction Balduf, Paul-Hermann High Energy Physics - Theory Mathematical Physics 81T15, 45M05, 81T17, 40G10 We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model. |
| title | Dyson-Schwinger Equations in Minimal Subtraction |
| topic | High Energy Physics - Theory Mathematical Physics 81T15, 45M05, 81T17, 40G10 |
| url | https://arxiv.org/abs/2109.13684 |