Vector Fields, Flows and Lie Groups of Diffeomorphisms
| dc.creator | Peterman, A. | |
| dc.date | 1999-12-15 | |
| dc.date.accessioned | 2026-07-07T12:26:46Z | |
| dc.date.available | 2026-07-07T12:26:46Z | |
| dc.description | The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical quantities. For the sake of simplicity, the case of a single $c$ is selected and chosen mass-independent if masslessness is not realized, this with the aim of expressing the effect of an infinitesimal change in $c$ on the computed observables. This change is found to be expressible in terms of an equation involving a vector field $V$ on the action's space $M$ (coordinates x). This equation is often referred to as ``evolution equation'' in physics. This vector field generates a one-parameter (here $c$) group of diffeomorphisms on $M$. Its flow $σ_c (x)$ can indeed be shown to satisfy the functional equation $$ σ_{c+t} (x) = σ_c (σ_t (x)) \equiv σ_c \circ σ_t $$ $$σ_0 (x) = x,$$ so that the very appearance of $V$ in the evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT. | |
| dc.description | (8 pages, latex) | |
| dc.identifier | https://arxiv.org/abs/hep-th/9912131 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9912131 | |
| dc.identifier | Eur.Phys.J.C14:705-708,2000 | |
| dc.identifier | doi:10.1007/s100520000375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214989 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Vector Fields, Flows and Lie Groups of Diffeomorphisms | |
| dc.type | text |